Electromagnetic Induction · Physics · Class 12
MCQ (Single Correct Answer)
A coil has 100 turns, each of area $0.05 \mathrm{~m}^2$ and total resistance $1.5 \Omega$. It is inserted at an instant in a magnetic field of 90 mT , with its axis parallel to the field. The charge induced in the coil at that instant is
Assertion (A): It is difficult to move a magnet into a coil of large number of turns when the circuit of the coil is closed.
Reason (R): The direction of induced current in a coil with its circuit closed, due to motion of a magnet, is such that it opposes the cause.
Two coils are placed near each other. When the current in one coil is changed at the rate of $5 \mathrm{~A} / \mathrm{s}$, an emf of 2 mV is induced in the other. The mutual inductance of the two coils is
A square shaped coil of side $$10 \mathrm{~cm}$$, having 100 turns is placed perpendicular to a magnetic field which is increasing at $$1 \mathrm{~T} / \mathrm{s}$$. The induced emf in the coil is
Subjective
(a) Show that the energy required to build up the current $I$ in a coil of inductance $L$ is $\frac{1}{2} L I^2$.
(b) Considering the case of magnetic field produced by air-filled current carrying solenoid, show that the magnetic energy density of a magnetic field $B$ is $\frac{B^2}{2 \mu_0}$.
(a) (i) State Lenz's Law. In a closed circuit, the induced current opposes the change in magnetic flux that produced it as per the law of conservation of energy. Justify.
(ii) A metal rod of length 2 m is rotated with a frequency $60 \mathrm{rev} / \mathrm{s}$ about an axis passing through its centre and perpendicular to its length. A uniform magnetic field of 2 T perpendicular to its plane of rotation is switched-on in the region. Calculate the e.m.f. induced between the centre and the end of the rod.
OR
(b) (i) State and explain Ampere's circuital law.
(ii) Two long straight parallel wires separated by 20 cm , carry 5 A and 10 A current respectively, in the same direction. Find the magnitude and direction of the net magnetic field at a point midway between them.
(a) (i) Define coefficient of self-induction. Obtain an expression for self-inductance of a long solenoid of length $$l$$, area of cross- section A having $$\mathbf{N}$$ turns.
(ii) Calculate the self-inductance of a coil using the following data of obtained when an AC source of frequency $$\left(\frac{200}{\pi}\right) \mathrm{~Hz}$$ and a DC source is applied across the coil.
| AC Source | ||
|---|---|---|
| S.No. | V (Volts) | I(A) |
| 1 | 3.0 | 0.5 |
| 2 | 6.0 | 1.0 |
| 3 | 9.0 | 1.5 |
| DC Source | ||
|---|---|---|
| S.No. | V (Volts) | I(A) |
| 1 | 4.0 | 1.0 |
| 2 | 6.0 | 1.5 |
| 3 | 8.0 | 2.0 |
OR
(b) (i) With the help of a labelled diagram, describe the principle and working of an ac generator. Hence, obtain an expression for the instantaneous value of the emf generated.
(ii) The coil of an ac generator consists of 100 turns of wire, each of area $$0.5 \mathrm{~m}^2$$. The resistance of the wire is $$100 \Omega$$. The coil is rotating in a magnetic field of $$0.8 \mathrm{~T}$$ perpendicular to its axis of rotation, at a constant angular speed of 60 radian per second. Calculate the maximum emf generated and power dissipated in the coil.
(ii) Calculation of self inductance:
| DC SOURCE | ||||
|---|---|---|---|---|
| S. No. | V(Volts) | I(Ampere) | Resistance (Ohms) | Average resistance value (R) |
| 1 | 4.0 | 1.0 | 4.0 | $$4.0\Omega$$ |
| 2. | 6.0 | 1.5 | 4.0 | |
| 3 | 8.0 | 2.0 | 4.0 | |
| AC SOURCE | ||||
|---|---|---|---|---|
| S. No. | V(Volts) | I(Ampere) | Impedance (Ohms) | Average Impedance value (Z) |
| 1 | 3.0 | 0.5 | 6.0 | $$6.0\Omega$$ |
| 2. | 6.0 | 1.0 | 6.0 | |
| 3 | 9.0 | 1.5 | 6.0 | |
(a) Consider the experimental set up shown in the figure. This jumping ring experiment is an outstanding demonstration of some simple laws of Physics. A conducting non-magnetic ring is placed over the vertical core of a solenoid. When current is passed through the solenoid, the ring is thrown off.
Answer the following questions :
(i) Explain the reason of jumping of the ring when the switch is closed in the circuit.
(ii) What will happen if the terminals of the battery are reversed and the switch is closed? Explain.
(iii) Explain the two laws that help us understand this phenomenon.
OR
(b) Briefly explain various ways to increase the strength of magnetic field produced by a given solenoid.
Two coils $$C_1$$ and $$C_2$$ are placed close to each other. The magnetic flux $$\phi_2$$ linked with the coil $$\mathrm{C}_2$$ varies with the current $$I_1$$ flowing in coil $$C_1$$, as shown in the figure. Find
(i) the mutual inductance of the arrangement, and
(ii) the rate of change of current $$\left(\frac{d \mathrm{I}_1}{d t}\right)$$ that will induce an emf of 100 V in coil C$$_2$$.