Moving Charges and Magnetism · Physics · MHT CET

A wire of length ' $L$ ' carries a current ' $I$ '. If the wire is turned into a square coil of single turn, the maximum magnitude of the torque in a given magnetic field $(\overrightarrow{\mathrm{B}})$ is

A circular coil carrying current has radius ' $R$ '. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{27}$ th of its value at the centre of the coil is

Lorentz magnetic force is acting on a particle of charge q moving with velocity $\vec{V}$ in a magnetic field $\vec{B}$. The work done by this force on the charged particle is

Two wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and same current is passed through them. Torque experienced by

An infinitely long straight conductor carrying current ' $I$ ' is bent into a shape as shown in figure. The radius of the circular loop is ' $r$ '. The magnetic induction at the centre of the loop at point ' O ' is

( $\mu_0=$ permeability of free space)

In the following figure magnitude of the magnetic field at the point $p$ is

A circular coil carrying current ' T ' has a radius ' $r$ ' and ' $n$ ' turns. The magnetic field along the axis of a coil at a distance ' $2 \sqrt{2} r$ ', from its centre is ( $\mu_0=$ permeability of free space, $n$ is very small)

The magnetic field intensity H at the centre of a long solenoid having $n$ turns per unit length and carrying a current I, when no material is kept in it is ( $\mu_0=$ permeability of free space)

Current $I$ is carried in a wire of length ' $L$ '. If wire is bent into a circular coil of single turn, the maximum torque in a given magnetic field $B$ is

A square of side ' $L$ ' metre lies in $x-y$ plane in a region where the magnetic field is $\overline{\mathrm{B}}$ and $\vec{B}=B_0(2 \hat{i}+3 \hat{j}+4 \hat{k})$, where $B_0$ is constant. The magnitude of flux passing through the square (in weber) is

A long straight wire of radius ' $r$ ' carries a steady current ' $I$ '. The current is uniformly distributed over its cross-section. The ratio $\left(\frac{B}{B_1}\right)$ of the magnetic field ' B ' and ' $\mathrm{B}_1$ ' at radial distances ' $\frac{r}{2}$ ' and ' $3 r$ respectively, from the axis of the wire is

In hydrogen atom, an electron of charge 'e' revolves in an orbit of radius ' $r$ ' with speed ' $v$ '. The magnetic moment associated with electron is

Two current carrying identical coils are kept as shown in figure. The magnetic field at centre ' O ' is ( N and R represent the number of turns and radius of each coil respectively, $\mu_0=$ permeability of free space)

The relation between magnetic moment $(\mathrm{M})$ of a current carrying circular coil and length (L) of the wire used is

A square coil ABCD of side ' L ' is carrying a current in clockwise direction. A straight conductor carrying current $\mathrm{I}_2$ (upward direction) is kept parallel to side AB at a distance $\frac{\mathrm{L}}{3}$ in the plane of $A B C D$. The net force on the coil ABCD is ( $\mu_0=$ magnetic permeability)

The magnetic field at the centre of a current carrying circular coil of area ' $A$ ' is ' $B$ '. The magnetic moment ( M ) of the coil is ( $\mu_0=$ permeability of free space)

Let the current ' $I$ ' be associated with an electron of charge ' $e$ ' moving in a circular orbit of radius ' $r$ ' with speed ' $v$ ' around the positively charged nucleus. The ratio $\frac{r}{v}$ is

A particle of charge $q$ moves with a velocity $\overrightarrow{\mathrm{V}}=a \hat{\mathrm{i}}$ in a magnetic field $\overrightarrow{\mathrm{B}}=b \hat{\mathrm{j}}+c \hat{\mathrm{k}}$, where ' $a$ ', ' b ' and ' c ' are constants. The magnitude of force experienced by particle is

Two similar wires of equal lengths are bent in the form of a square and a circular loop. They are suspended in a uniform magnetic field and same current is passed through them. Torque experienced by

A wire of length $L$ carries current $I$ along x - axis. A magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0(\hat{\mathrm{i}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}) \mathrm{T}$ acts on the wire. The magnitude of magnetic force acting on the wire is

A circular coil of wire consisting of ' $n$ ' tums each of radius 8 cm carries a current of 0.4 A . The magnitude of the magnetic field at the centre of coil is $3.14 \times 10^{-4} \mathrm{~T}$. The value of ' $n$ ' is

[Take $\mu_0=12.56 \times 10^{-7}$ SI unit]

The wire loop PQRSP formed by joining two semicircular wire of radii $R_1$ and $R_2$ carries a current $I$ as shown. The magnitude of the magnetic field at the centre ' O ' is

A coil having 9 turns carrying current produces magnetic field $B_1$ at the centre. Now that coil is rewounded into 3 turns carrying same current. Then magnetic field at the centre $B_2$ is

An electron moves in Bohr orbit. The magnetic field at the centre is proportional to

Two long parallel wires carry currents $I_1$ and $\mathrm{I}_2\left(\mathrm{I}_1>\mathrm{I}_2\right)$. When currents are flowing in the same direction, the magnetic field at a point midway between the wires is $6 \times 10^{-6} \mathrm{~T}$. If the direction of $\mathrm{I}_2$ is reversed the field at midpoint becomes $3 \times 10^{-5} \mathrm{~T}$. The ratio $\mathrm{I}_1: \mathrm{I}_2$ is

Two very long straight conductors (wires) are set parallel to each other. Each carries a current ' I ' in the same direction and the separation between them is ' 2 r '. The intensity of the magnetic field at point ' P ' (as shown in the figure) ( $\mu_0=$ permeability of free space) is

Two identical long parallel wires carry currents ' $\mathrm{I}_1$ ' and ' $\mathrm{I}_2$ ' such that $\mathrm{I}_1>\mathrm{I}_2$. When the currents are in the same direction, the magnetic field at a point midway between the wires is $8 \times 10^{-6} \mathrm{~T}$. If the direction of $\mathrm{I}_2$ is reversed, the field becomes $3.2 \times 10^{-5} \mathrm{~T}$. The ratio of $\mathrm{I}_2$ to $\mathrm{I}_1$ is

An element $\overrightarrow{\Delta l}=\Delta \mathrm{xi}$ is placed at the origin and carries a current of 10 A . The magnitude of magnetic field on the Y axis at a distance of 0.5 m if $\Delta x=1 \mathrm{~cm}$ is $\left(\frac{\mu_0}{4 \pi}=10^{-7}\right.$ SI unit $)\left(\sin 90^{\circ}=1\right)$

A current ' I ' is flowing in a conductor PQRST as shown in figure. The radius of curved path QRS is ' R ' and length of straight portion PQ and ST is very large. The magnetic field at the centre $[\mathrm{O}]$ of the curved part is ( $\mu_0=$ permeability of free space)

A wire has three different sections as shown in figure. The magnitude of the magnetic field produced at the centre ' $O$ ' of the semicircle by three sections together is ( $\mu_0=$ permiability of free space)

A long wire carrying a steady current is bent into a circle of single turn. The magnetic field at the centre of the coil is ' B '. If it is bent into a circular loop of radius ' $\mathrm{r}_1$ ' having ' n ' turns, the magnetic field at the centre of the coil for same current is

A particle carrying a charge equal to 1000 times the charge on an electron, is rotating one rotation per second in a circular path of radius ' $r$ ' $m$. If the magnetic field produced at the centre of the path is $x$ times the permeability of vacuum, the radius ' r ' in m is $\left[\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\right]\left[\mathrm{x}=2 \times 10^{-16}\right]$

Bohr model is applied to a particle of mass m and charge $q$ is moving in a plane under the influence of a transverse magnetic field (B). The energy of the charged particle in the second level will be ( $\mathrm{h}=$ Planck's constant)

Two long conductors separated by a distance ' d ' carry currents ' $\mathrm{I}_1$ ' and ' $\mathrm{I}_2$ ' in the same directions. They exert a force ' $F$ ' on each other. The distance between them is increased to ' 3 d '. If new repulsive force of magnitude ' $\frac{2}{3} \mathrm{~F}$ ' is found between these conductors, the required change in the magnitude and direction of one of the currents in the conductor is respectively [length of the conductors is constant]

An arc of a circle of radius ' $R$ ' subtends an angle $\frac{\pi}{2}$ at the centre. It carries a current $I$. The magnetic field at the centre will be ( $\mu_0=$ permeability of free space)

A current 'I' flows in anticlockwise direction in a circular arc of a wire having $\left(\frac{3}{4}\right)^{\text {th }}$ of circumference of a circle of radius R. The magnetic field ' $B$ ' at the centre of circle is ( $\mu_0=$ permeability of free space)

The magnetic induction along the axis of a toroidal solenoid is independent of

Two coils P and Q each of radius R carry currents I and $\sqrt{8} \mathrm{I}$ respectively in same direction. Those coils are lying in perpendicular planes such that they have a common centre. The magnitude of the magnetic field at the common centre of the two coils is ( $\mu_0=$ permeability of free space)

Two concentric circular coils A and B having radii 20 cm and 10 cm respectively lie in the same plane. The current in coil A is 0.5 A in anticlockwise direction. The current in coil B , so that net magnetic field at the common centre is zero, is

An electron is revolving in a circular orbit of radius $r$ in a hydrogen atom. The angular momentum of the electron is L . The relation between dipole moment (m) associated with it, gyromagnetic ratio ( R ) and L is

Three infinite straight wires $\mathrm{A}, \mathrm{B}$ and C carry currents as shown in figure. The resultant force on wire $B$ is directed

Two parallel wires separated by distance 'b' are carrying equal current ' $I$ ' in the same direction. The force per unit length of the wire is

Magnetic induction produced at the centre of a circular loop of radius ' $R$ ' carrying a current is ' B '. The magnetic moment of the loop is ( $\mu_0=$ permeability of free space)

The strength of magnetic field at a perpendicular distance ' $x$ ' near a long straight conductor carrying current ' I ' is ' B '. The magnetic field at a distance $\frac{x}{3}$ from straight conductor will be

An infinitely long straight conductor carrying current 'I' is bent in a shape as shown in figure. The radius of the circular part of loop is 'r'. The magnetic induction at the centre 'C' is ($\mu=$ permeability of free space)

A current carrying circular loop of radius ' $R$ ' and current carrying long straight wire are placed in the same plane. The current through circular loop and long straight wire are ' $I_c$ ' and ' $\mathrm{I}_{\mathrm{w}}$ ' respectively. The perpendicular distance between centre of the circular loop and wire is ' d '. The magnetic field at the centre of the loop will be zero when separation ' $d$ ' is equal to

Magnetic field at the centre of a circular loop of area ' $A$ ' is ' $B$ '. The magnetic moment of the loop will be

A boat is moving due east in a region where the earth's magnetic field is $3.6 \times 10^{-5} \mathrm{~N} / \mathrm{Am}$ due north and horizontal. The boat carries a vertical conducting rod 2 m long. If the speed of the boat is $2.00 \mathrm{~m} / \mathrm{s}$, the magnitude of the induced e.m.f. in the rod is

The magnetic flux near the axis and inside the air core solenoid of length 80 cm carrying current ' I ' is $1.57 \times 10^{-6} \mathrm{~Wb}$. Its magnetic moment will be [cross-sectional area of a solenoid is very small as compared to its length, $\mu_0=4 \pi \times 10^{-7}$ SI unit $](\pi=3.14)$

Two long straight parallel wires are separated by a distance '2d'. Each wire carries a current 'I' in the same direction. The magnetic field at a point 'P' midway between them is

The magnitude of magnetic field at point 'O' in the following figure will be

A coil of ' $n$ ' turns and radius ' $R$ ' carries a current 'I'. It is unwound and rewound to make a new coil of radius $\frac{R}{3}$ and the same current is passed through it. The ratio of the magnetic moment of the new coil to that of the original coil is

A charged particle is moving in a uniform magnetic field in a circular path of radius ' $R$ '. When the kinetic energy of the particle is increased to three times, then the new radius will be

A circular arc of radius r carrying current ' I ' subtends an angle $\frac{\pi}{8}$ at its entre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is ( $\mu_0=$ permeability of free space)

Electron of mass ' $m$ ' and charge ' $q$ ' is travelling with speed ' $v$ ' along a circular path of radius ' $R$ ' at right angles to a uniform magnetic field of intensity ' B '. If the speed of the electron is halved and the magnetic field is doubled, the resulting path would have radius

A current carrying circular loop of radius ' $R$ ' and current carrying long straight wire are placed in the same plane. $I_c$ and $I_w$ are the currents through circular loop and long straight wire respectively. The perpendicular distance between centre of the circular loop and wire is ' d '. The magnetic field at the centre of the loop will be zero when separation ' $d$ ' is equal to

A long solenoid carrying a current produces magnetic field B along its axis. If the number of turns per cm are tripled and the current is made $\left(\frac{1}{4}\right)^{\text {th }}$ then the new value of magnetic field will be

The magnetic potential energy stored in certain inductor is $64 \times 10^{-3} \mathrm{~J}$, when the current in the inductor is 80 mA . This inductor is of inductance

The magnetic induction due to an ideal solenoid is independent of

The magnetic field intensity inside current carrying solenoid is $\mathrm{H}=2.4 \times 10^3 \mathrm{~A} / \mathrm{m}$. If length and number of turns of a solenoid is 15 cm and 60 turns respectively. The current flowing in the solenoid is

A particle carrying a charge equal to 100 times the charge on an electron is rotating one rotation per second in a circular path of radius 0.8 m . The value of magnetic field produced at the centre will be ( $\mu_0=$ permeability of vacuum)

A charged particle of charge ' $q$ ' is accelerated by a potential difference ' $V$ ' enters a region of uniform magnetic field ' $B$ ' at right angles to the direction of field. The charged particle completes semicircle of radius ' $r$ ' inside magnetic field. The mass of the charged particle is

A charged particle is moving in a uniform magnetic field in a circular path with radius ' $R$ '. When the energy of the particle is doubled, then the new radius will be

A massless square loop of wire of resistance ' $R$ ' supporting a mass ' M ' hangs vertically with one of its sides in a uniform magnetic field ' B ' directed outwards in the shaded region. A d.c. voltage ' V ' is applied to the loop. For what value of ' $V$ ' the magnetic force will exactly balance the weight of the supporting mass ' M '? (side of loop = L, $\mathrm{g}=$ acceleration due to gravity)

A thin ring of radius ' $R$ ' carries a uniformly distributed charge. The ring rotates at constant speed ' $N$ ' r.p.s. about its axis perpendicular to the plane. If ' $B$ ' is the magnetic field at the centre, the charge on the ring is ( $\mu_0=$ permeability of free space)

A charged particle is moving along a magnetic field line. What is the magnetic force acting on the particle? $\left(\sin 0^{\circ}=0, \sin \frac{\pi}{2}=1\right)$

A current of 5 A flows through a toroid having a core of mean radius 20 cm . If 4000 turns of the conducting wire are wound on the core, then the magnetic field inside the core of the toroid is [permeability of free space $=4 \pi \times 10^{-7}$ SI units]

A particle having a charge 50 e is revolving in a circular path of radius 0.4 m with $1 \mathrm{r} . \mathrm{p} . \mathrm{s}$. The magnetic field produced at the centre of the circle is $\left(\mu_0=4 \pi \times 10^{-7}\right.$ SI units and $e=1.6 \times 10^{-19} \mathrm{c}$)

Three long, straight parallel wires carrying currents are arranged as shown. The wire C which carries a current of 5.0 A is so placed that it experiences no force. The distance of wire C from wire $D$ is

Cyclotron is used to

The magnetic field at the centre of a current carrying circular coil of area ' $A$ ' is ' $B$ '. The magnetic moment of the coil is ( $\mu_0=$ permeability of free space)

Two identical current carrying coils with same centre are placed with their planes perpendicular to each other. If current $\mathrm{I}=\sqrt{2} \mathrm{~A}$ and radius of the coil is $R=1 \mathrm{~m}$, then magnetic field at centre is equal to ( $\mu_0=$ permeability of free space)

Figure shows two semicircular loops of radii $$R_1$$ and $$R_2$$ carrying current $I$. The magnetic field at the common centre '$$\mathrm{O}$$' is

A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having $$\mathrm{n}$$ turns. If the same current passes in both the cases, the ratio of magnetic fields produced at the centre for one turn to that of $$n$$ turns is

A horizontal wire of mass '$$m$$', length '$$l$$' and resistance '$$R$$' is sliding on the vertical rails on which uniform magnetic field '$$B$$' is directed perpendicular. The terminal speed of the wire as it falls under the force of gravity is ( $$\mathrm{g}=$$ acceleration due to gravity)

A straight wire carrying a current (I) is turned into a circular loop. If the magnitude of the magnetic moment associated with it is '$$M$$', then the length of the wire will be

A solenoid of length $$0.4 \mathrm{~m}$$ and having 500 turns of wire carries a current $$3 \mathrm{~A}$$. A thin coil having 10 turns of wire and radius $$0.1 \mathrm{~m}$$ carries current $$0.4 \mathrm{~A}$$. the torque required to hold the coil in the middle of the solenoid with its axis perpendicular to the axis of the solenoid is $$\left(\mu_0=4 \pi \times 10^{-7}\right.$$ SI units, $$\left.\pi^2=10\right)\left(\sin 90^{\circ}=1\right)$$

Two circular coils made from same wire but radius of $$1^{\text {st }}$$ coil is twice that of $$2^{\text {nd }}$$ coil. If magnetic field at their centres is same then ratio of potential difference applied across them is ($$1^{\text {st }}$$ to $$2^{\text {nd }}$$ coil)

The ratio of magnetic field at the centre of the current carrying circular loop and magnetic moment is $$X$$. When both the current and radius are doubled, then the ratio will be

A circular current carrying coil has radius $$R$$. The magnetic induction at the centre of the coil is $$B_C$$. The magnetic induction of the coil at a distance $$\sqrt{3} R$$ from the centre along the axis is $$B_A$$. The ratio $$B_A: B_C$$ is

A circular coil of radius '$$r$$' and number of turns ' $n$ ' carries a current '$$I$$'. The magnetic fields at a small distance '$$h$$' along the axis of the coil $$\left(B_a\right)$$ and at the centre of the coil $$\left(\mathrm{B}_{\mathrm{c}}\right)$$ are measured. The relation between $$B_c$$ and $$B_a$$ is

Two concentric circular coils A and B have radii $$20 \mathrm{~cm}$$ and $$10 \mathrm{~cm}$$ respectively lie in the same plane. The current in coil A is $$0.5 \mathrm{~A}$$ in anticlockwise direction. The current in coil B so that net field at the common centre is zero, is

Two concentric circular coils of 10 turns each are situated in the same plane. Their radii are $$20 \mathrm{~cm}$$ and $$40 \mathrm{~cm}$$ and they carry respectively $$0.2 \mathrm{~A}$$ and $$0.3 \mathrm{~A}$$ current in opposite direction. The magnetic field at the centre is ($$\mu_0=4 \pi \times 10^{-7}$$ SI units)

A coil of '$$n$$' turns and radius '$$R$$' carries a current '$$I$$'. It is unwound and rewound again to make another coil of radius $$\left(\frac{\mathrm{R}}{3}\right)$$, current remaining the same. The ratio of magnetic moment of the new coil to that of original coil is

An electron makes a full rotation in a circle of radius $$0.8 \mathrm{~m}$$ in one second. The magnetic field at the centre of the circle is $$\left(\mu_0=4 \pi \times 10^{-7}\right.$$ SI units)

$$\mathrm{A}, \mathrm{B}$$ and $$\mathrm{C}$$ are three parallel conductors of equal lengths and carry currents I, I and 2I respectively as shown in figure. Distance $$A B$$ and $$B C$$ is same as '$$d$$'. If '$$F_1$$' is the force exerted by $$\mathrm{B}$$ on $$\mathrm{A}$$ and $$\mathrm{F}_2$$ is the force exerted by $$\mathrm{C}$$ on $$\mathrm{A}$$, then

The magnetic moment of a current (I) carrying circular coil of radius '$$r$$' and number of turns '$$n$$' depends on

Two similar coils each of radius $$\mathrm{R}$$ are lying concentrically with their planes at right angles to each other. The current flowing in them are I and 2I. The resultant magnetic field of induction at the centre will be $$\left(\mu_0=\right.$$ Permeability of vacuum)

A single turn current loop in the shape of a right angle triangle with side $$5 \mathrm{~cm}, 12 \mathrm{~cm}, 13 \mathrm{~cm}$$ is carrying a current of $$2 \mathrm{~A}$$. The loop is in a uniform magnetic field of magnitude $$0.75 \mathrm{~T}$$ whose direction is parallel to the current in the $$13 \mathrm{~cm}$$ side of the loop. The magnitude of the magnetic force on the $$5 \mathrm{~cm}$$ side will be $$\frac{\mathrm{x}}{130} \mathrm{~N}$$. The value of '$$x$$' is

Two long conductors separated by a distance '$$\mathrm{d}$$' carry currents $$I_1$$ and $$I_2$$ in the same direction. They exert a force '$$F$$' on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance between them is also increased to $$3 \mathrm{~d}$$. The new value of force between them is

A circular arc of radius '$$r$$' carrying current '$$\mathrm{I}$$' subtends an angle $$\frac{\pi}{16}$$ at its centre. The radius of a metal wire is uniform. The magnetic induction at the centre of circular arc is $$\left[\mu_0=\right.$$ permeability of free space]

A cylindrical magnetic rod has length $$5 \mathrm{~cm}$$ and diameter $$1 \mathrm{~cm}$$. It has uniform magnetization $$5.3 \times 10^3 \mathrm{~A} / \mathrm{m}^3$$. Its net magnetic dipole moment is nearly

Two parallel wires of equal lengths are separated by a distance of $$3 \mathrm{~m}$$ from each other. The currents flowing through $$1^{\text {st }}$$ and $$2^{\text {nd }}$$ wire is $$3 \mathrm{~A}$$ and 4.5 A respectively in opposite directions. The resultant magnetic field at mid point between the wires $$\left(\mu_0=\right.$$ permeability of free space)

An electron is projected along the axis of circular conductor carrying current I. Electron will experience

The magnetic field at the centre of a circular coil of radius '$$R$$', carrying current $$2 A$$ is '$$B_1$$'. The magnetic field at the centre of another coil of radius '$$3 R$$' carrying current $$4 A$$ is '$$B_2$$'. The ratio $$B_1:B_2$$ is

Two wires $$2 \mathrm{~mm}$$ apart supply current to a $$100 \mathrm{~V}, 1 \mathrm{~kW}$$ heater. The force per metre between the wires is ( $$\mu_0=4 \pi \times 10^{-27}$$ SI unit)

Two long parallel wires carrying currents $$8 \mathrm{~A}$$ and $$15 \mathrm{~A}$$ in opposite directions are placed at a distance of $$7 \mathrm{~cm}$$ from each other. A point '$$\mathrm{P}$$' is at equidistant from both the wires such that the lines joining the point to the wires are perpendicular to each other. The magnitude of magnetic field at point '$$\mathrm{P}$$' is $$(\sqrt{2}=1.4) ( \mu_0=4 \pi \times 10^{-7}$$ SI units)

Electron of mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$' is travelling with speed '$$v$$' along a circular path of radius '$$R$$', at right angles to a uniform magnetic field of intensity '$$B$$'. If the speed of the electron is halved and the magnetic field is doubled, the resulting path would have radius

10 A current is flowing in two straight parallel wires in the same direction. Force of attraction between them is $$1 \times 10^{-3} \mathrm{~N}$$. If the current is doubled in both the wires the force will be

The magnetic field at a point $$\mathrm{P}$$ situated at perpendicular distance '$$R$$' from a long straight wire carrying a current of $$12 \mathrm{~A}$$ is $$3 \times 10^{-5} \mathrm{~Wb} / \mathrm{m}^2$$. The value of '$$\mathrm{R}$$' in $$\mathrm{mm}$$ is $$\left[\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{Am}\right]$$

A long straight wire carrying a current of $$25 \mathrm{~A}$$ rests on the table. Another wire PQ of length $$1 \mathrm{~m}$$ and mass $$2.5 \mathrm{~g}$$ carries the same current but in the opposite direction. The wire PQ is free to slide up and down. To what height will wire PQ rise? ($$\mu_0=4 \pi \times 10^{-7}$$ SI unit)

Two parallel conducting wires of equal length are placed distance 'd' apart, carry currents '$$\mathrm{I}_1$$' and '$$\mathrm{I}_2$$' respectively in opposite directions. The resultant magnetic field at the midpoint of the distance between both the wires is

An electron and a proton having the same momenta enter perpendicularly into a magnetic field. What are their trajectories in the field?

A solenoid 2 m long and 4 cm in diameter has 4 layers of windings of 1000 turns each and carries a current of 5 A. What is the magnetic field at its centre along the axis? [$$\mu_0=4\pi\times10^{-7}$$ Wb/Am]

A particle of charge 'q' and mass 'm' moves in a circular orbit of radius 'r' with angular speed '$$\omega$$'. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

A current carrying loop is placed in a uniform magnetic field. The torque acting on the loop does not depend upon

Two long conductors, separated by a distance '$$\mathrm{d}$$' carry currents '$$\mathrm{I}_1$$' and '$$\mathrm{I}_2$$' in the same directions. They exert a force '$$\mathrm{F}$$' on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to '$$3 \mathrm{~d}$$'. The new value of the force between them is

An electron in a circular orbit of radius $$0.05 \mathrm{~nm}$$ performs $$10^{14}$$ revolutions/second. What is the magnetic moment due to the rotation of electron? $$(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C})$$

A long solenoid carrying current $$\mathrm{I}_1$$ produces magnetic field $$\mathrm{B}_1$$ along its axis. If the current is reduced to $$20 \%$$ and number of turns per $$\mathrm{cm}$$ are increased five times then new magnetic field B$$_2$$ is equal to

A straight wire of diameter $$0.4 \mathrm{~mm}$$ carrying a current of $$2 \mathrm{~A}$$ is replaced by another wire of 0.8 $$\mathrm{mm}$$ diameter carrying the same current. The magnetic field at distance $$(\mathrm{R})$$ from both the wires is 'B$$_1$$' and 'B$$_2$$' respectively. The relation between B$$_1$$ and B$$_2$$ is

An electron is projected along the axis of circular conductor carrying current '$$\mathrm{I}$$' The electron will experience

A thin ring of radius '$$R$$' meter has charge '$$q$$' coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of $$f$$ revolution/s. The value of magnetic induction in $$\mathrm{Wb} \mathrm{m}^{-2}$$ at the center of the ring is ($$\mu_0=$$ Permeability of free space)

A particle having a charge $$100 \mathrm{e}$$ is revolving in a circular path of radius $$0.8 \mathrm{~m}$$ with 1. r.p.s The magnetic field produced at the centre of the circle in SI unit is $$\left(\mu_0=\right.$$ permeability of vacuum, $$e= \left.1.6 \times 10^{-19} \mathrm{C}\right)$$

The magnetic field inside a current carrying toroidal solenoid is $$0.2 \mathrm{~mT}$$. What is the magnetic field inside the toroid if the current through it is tripled and radius is made $$\frac{1}{3}^{\text {rd}}$$ ?

When a battery is connected to the two ends of a diagonal of a square conductor frame of side '$$a$$', the magnitude of magnetic field at the centre will be ( $$\mu_0=$$ permeability of free space)

Two concentric coplanar circular loops of radii '$$r{ }_1$$' and '$$r_2$$' respectively carry currents '$$i_1$$' and '$$\mathrm{i}_2$$' in opposite directions (one clockwise and other anticlockwise). The magnetic induction at the centre of the loops is half that due to '$$i_1$$' alone at the centre. If $$r_2=2 r_1$$, the value of $$\frac{i_2}{i_1}$$

Assuming the atom is in the ground state, the expression for the magnetic field at a point nucleus in hydrogen atom due to circular motion of electron is [$$\mu_0=$$ permeability of free space, $$\mathrm{m}=$$ mass of electron, $$\epsilon_0=$$ permittivity of free space, $$\mathrm{h}=$$ Planck's constant ]

A, B and C are three parallel conductors of equal lengths carrying currents $$\mathrm{I}, \mathrm{I}$$ and $$2 \mathrm{I}$$ respectively. Distance between A and B is '$$x$$' and that between B and C is also '$$x$$'. $$F_1$$ is the force exerted by conductor $$\mathrm{B}$$ on $$\mathrm{A}$$. $$\mathrm{F}_2$$ is the force exerted by conductor $$\mathrm{C}$$ on $$\mathrm{A}$$. Current $$\mathrm{I}$$ in $$\mathrm{A}$$ and $$\mathrm{I}$$ in $$\mathrm{B}$$ are in same direction and current $$2 \mathrm{I}$$ in $$\mathrm{C}$$ is in opposite direction. Then

Magnetic moment of revolving electron of charge (e) and mass (m) in terms of angular momentum (L) of electron is :

The magnetic flux near the axis and inside the air core solenoid of length $$60 \mathrm{~cm}$$ carrying current '$$\mathrm{I}$$' is $$1.57 \times 10^{-6} \mathrm{~Wb}$$. Its magnetic moment will be $$\left[\mu_0=4 \pi \times 10^{-7}\right.$$, SI unit and crosssectional area is very small as compared to length of solenoid.]

A charge moves with velocity '$$V$$' through electric field $$(E)$$ as well as magnetic field (B). then the force acting on it is

A long solenoid carrying a current produces a magnetic field B along its axis. If the number of turns per $$\mathrm{cm}$$ is doubled and the current is made $$\left(\frac{1}{3}\right)^{\text {rd }}$$ then the new value of the magnetic field will be

A metal conductor of length $$1 \mathrm{~m}$$ rotates vertically about one of its ends at an angular velocity of $$5 \mathrm{~rad} / \mathrm{s}$$. If horizontal component of earth's magnetic field is $$0.2 \times 10^{-4} \mathrm{~T}$$, then the e.m.f. developed between the two ends of the conductor is

Two wires carrying currents $$5 \mathrm{~A}$$ and $$2 \mathrm{~A}$$ are enclosed in a circular loop as shown in the figure. Another wire carrying a current of $$3 \mathrm{~A}$$ is situated outside the loop. The value of $$\oint \overrightarrow{\mathrm{B}} \overrightarrow{\mathrm{d} l}$$ around the loop is ( $$\mu_0=$$ permeability of free space, $$\overrightarrow{\mathrm{d} l}$$ is the length of the element on the Amperion loop)

The magnetic field at the centre of a current carrying circular coil of area 'A' is 'B'. The magnetic moment of the coil is ( $$\mu_0=$$ permeability of free space)

The relation between magnetic moment 'M' of revolving electron and principle quantum number 'n' is

If the charge to ratio of an electron is 'A' C/kg, then the gyromagnetic ratio of an orbital electron in C/kg is

The magnetic field intensity 'H' at the centre of a long solenoid having 'n' turns per unit length and carrying a current 'I', when no material is kept in it, is

An electron (e) moves in circular orbit of radius 'r' with uniform speed 'V'. It produces magnetic field 'B' at the centre of circle. The magnetic field B is $$\left(\mu_0=\right.$$ permeability of free space)

An electron moves in a circular orbit with uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is [ $\mu_0=$ permeability of free space, $e=$ electronic charge]

A circular coil of radius $$R$$ is carrying a current $$I_1$$ in anti-clockwise sense. A long straight wire is carrying current $$I_2$$ in the negative direction of $$X$$-axis. Both are placed in the same plane and the distance between centre of coil and straight wire is $$d$$. The magnetic field at the centre of coil will be zero for the value of $$d$$ equal to

An $$\alpha$$-particle of energy 10 eV is moving in a circular path in uniform magnetic field. The energy of proton moving in the same path and same magnetic field will be [mass of $$\alpha$$-particle $$=4$$ times mass of proton]

An electron $$(e)$$ is revolving in a circular orbit of radius $$r$$ in hydrogen atom. The angular momentum of the electron is ($$M=$$ magnetic dipole moment associated with it and $$m=$$ mass of electron)

A charged particle is moving in a uniform magnetic field in a circular path of radius $$R$$. When the energy of the particle becomes three times the original, the new radius will be

A charge $$q$$ moves with velocity $$v$$ through electric field $$\mathrm{E}$$ as well as magnetic field (B). Then, the force acting on it is

Maximum kinetic energy gained by the charged particle in the cyclotron is independent of

In a hydrogen atom, an electron of charge $e$ revolves in a orbit of radius $r$ with speed $v$. Then, magnetic moment associated with electron is

Six very long insulated copper wires are bound together to form a cable. The currents carried by the wires are $I_1=+10 \mathrm{~A}, I_2=-13 \mathrm{~A}, I_3=+10$ $\mathrm{A}, I_4=+7 \mathrm{~A}, I_5=-12 \mathrm{~A}$ and $I_6=+18 \mathrm{~A}$. The magnetic induction at a perpendicular distance of 10 cm from the cable is $\left(\mu_0=4 \pi \times 10^{-7} \mathrm{~Wb} / \mathrm{A}-\mathrm{m}\right)$

A circular coil and a square coil is prepared from two identical metal wires and a current is passed through it. Ratio of magnetic dipole moment associated with circular coil to that of square coil is

Figure show the circular coil carrying current $I$ kept very close but not touching at a point $A$ on a straight conductor carrying the same current $I$. The magnitude of magnetic induction at the centre of the circular coil will be

Torque acting on a rectangular coil carrying current ' $l$ ' situated parallel to magnetic field of induction ' $B$ ', having number of turns ' $n$ ' and area ' $A$ ' is

A circular coil of wire consisting of 100 turns each of radius 9 cm carries a current of 0.4 A . The magnitude of the magnetic field at the centre of coil is $\left[\mu_0=12.56 \times 10^{-7} \mathrm{SI}\right.$ Unit]

The magnetic dipole moment of a short magnetic dipole at a distant point along the equator of magnet has a magnitude of ' $X$ ' in SI units. If the distance between the point and the magnet is halved then the magnitude of dipole moment will be

Two parallel conductors carrying unequal currents in the same direction ............

The magnitude of the magnetic induction at a point on the axis at a large distance ( $r$ ) from the centre of a circular coil of ' $n$ ' turns and area ' $A$ ' carrying current ( $I$ ) is given by