Magnetic Effect of Current · Physics · Class 12

A 1 cm segment of a wire lying along $x$-axis carries current of 0.5 A along $+x$ direction. A magnetic field $\vec{B}=(0.4 \mathrm{mT}) \hat{j}+(0.6 \mathrm{mT}) \hat{k}$ is switched on, in the region. The force acting on the segment is

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m . The number of turns in the solenoid should be

Assertion (A) : The deflection in a galvanometer is directly proportional to the current passing through it.

Reason (R) : The coil of a galvanometer is suspended in a uniform radial magnetic field.

A particle of mass $m$ and charge $q$ describes a circular path of radius $R$ in a magnetic field. If its mass and charge were $2 m$ and $\frac{q}{2}$ respectively, the radius of its path would be

Assertion (A): The energy of a charged particle moving in a magnetic field does not change.

Reason (R): It is because the work done by the magnetic force on the charge moving in a magnetic field is zero.

A long straight wire of radius '$$a$$' carries a steady current $$I$$. The current is uniformly distributed across its area of cross-section. The ratio of magnitude of magnetic field $$\vec{B}_1$$ at $$\frac{a}{2}$$ and $$\vec{B}_2$$ at distance $$2 a$$ is

Two long parallel wires kept $$2 \mathrm{~m}$$ apart carry $$3 \mathrm{~A}$$ current each, in the same direction. The force per unit length on one wire due to the other is

Assertion (A): The deflecting torque acting on a current carrying loop is zero when its plane is perpendicular to the direction of magnetic field.

Reason (R): The deflecting torque acting on a loop of magnetic moment $$\vec{m}$$ in a magnetic field $$\vec{B}$$ is given by the dot product of $$\vec{m}$$ and $$\vec{B}$$.

Using Biot-Savart law, derive expression for the magnetic field $(B)$ due to a circular current carrying loop at a point on its axis and hence at its centre.

(a) (i) A proton moving with velocity $\vec{V}$ in a non. uniform magnetic field traces a path as shown in the figure.

The path followed by the proton is always in the plane of the paper. What is the direction of the magnetic field in the region near points $P, Q$ and $R$ ? What can you say about relative magnitude of magnetic fields at these points?

(ii) A current carrying circular loop of area $A$ produces a magnetic field $B$ at its centre. Show that the magnetic moment of the loop is $\frac{2 B A}{\mu_0} \sqrt{\frac{A}{\pi}}$

OR

(b) (i) Derive an expression for the torque acting on a rectangular current loop suspended in a uniform magnetic field.

(ii) A charged particle is moving in a circular path with velocity $\vec{V}$ in a uniform magnetic field $\vec{B}$. It is made to pass through a sheet of lead and as a consequence, it looses one half of its kinetic energy without change in its direction. How will (1) the radius of its path (2) its time period of revolution change?

Derive an expression for magnetic force $\vec{F}$ acting on a straight conductor of length $L$ carrying current I in an external magnetic field $\vec{B}$. Is it valid when the conductor is in zig-zag form? Justify.

An electron moving with a velocity $\vec{v}=\left(1.0 \times 10^7\right.$ $\mathrm{m} / \mathrm{s}) \hat{i}+\left(0.5 \times 10^7 \mathrm{~m} / \mathrm{s}\right) \hat{j}$ enters a region of uniform magnetic field $\vec{B}=(0.5 \mathrm{mT}) \hat{j}$. Find the radius of the circular path described by it. While rotating; does the electron trace a linear path too? If so, calculate the linear distance covered by it during the period of one revolution.

(a) Write the expression for the Lorentz force on a particle of charge $$q$$ moving with a velocity $$\vec{v}$$ in a magnetic field $$\vec{B}$$. When is the magnitude of this force maximum? Show that no work is done by this force on the particle during its motion from a point $$\vec{r_1} \text { to point } \vec{r}_2 \text {. }$$

OR

(b) A long straight wire $$A B$$ carries a current I. A particle (mass $$m$$ and charge $$q$$ ) moves with a velocity $$\vec{v}$$, parallel to the wire, at a distance $$d$$ from it as shown in the figure. Obtain the expression for the force experienced by the particle and mention its directions.