The graph gives the magnitude B(t) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first

(1) b > (d = e) < (a = c)

(2) b > (d = e) > (a = c)

(3) b < d < e < c < a

(4) b > (a = c) > (d = e)

A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be –

1. halved                           

2. the same

3. doubled                         

4. quadrupled

Two circular coils can be arranged in any of the three situations shown in the figure. Their mutual inductance will be 

(1) Maximum in situation (A)

(2) Maximum in situation (B)

(3) Maximum in situation (C)

(4) The same in all situations

An aluminum ring B faces an electromagnet A. The current I through A can be altered. Then :

(1) Whether I increases or decreases, B will not experience any force

(2) If I decrease, A will repel B

(3) If I increases, A will attract B

(4) If I increases, A will repel B

Figure shows three regions of magnetic field, each of area A, and in each region magnitude of magnetic field decreases at a constant rate $\mathrm{\alpha }$.

If $\overrightarrow{\mathrm{E}}$ is induced electric field then value of line integral $\int \overrightarrow{\mathrm{E}}.\mathrm{d}\overrightarrow{\mathrm{r}}$ along the given loop is equal to

1.  $\mathrm{\alpha A}$                             

2.  $-\mathrm{\alpha A}$

3.  $3\mathrm{\alpha A}$                           

4.  $-3\mathrm{\alpha A}$

The magnitude of the earth’s magnetic field at a place is B₀ and the angle of dip is δ. A horizontal conductor of length l lying along the magnetic north-south moves eastwards with a velocity v. The emf induced across the conductor is 

(1) Zero

(2) B₀lv sinδ

(3) B₀lv

(4) B₀lv cosδ

The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current through the battery (i) just after the switch is closed and (ii) a long time later, greatest first

(1) (i) i₂ > i₃ > i₁ (i₁ = 0) (ii) i₂ > i₃ > i₁

(2) (i) $i_2<i_3<i_1(i_1\ne 0)$ (ii) i₂ > i₃ > i₁

(3) (i) i₂ = i₃ = i₁ (i₁ = 0) (ii) i₂ < i₃ < i₁

(4) (i) $i_2=i_3>i_1(i_1\ne 0)$ (ii) i₂ > i₃ > i₁

An e.m.f. of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time t = ∞ and at t = 1 second is 

(1) $\frac{e^{1/2}}{e^{1/2}-1}$

(2) $\frac{e^2}{e^2-1}$

(3) 1 – e^–1

(4) e^–1

Consider the situation shown in the figure. The wire AB is sliding on the fixed rails with a constant velocity. If the wire AB is replaced by semicircular wire, the magnitude of the induced current will 

(1) Increase

(2) Remain the same

(3) Decrease

(4) Increase or decrease depending on whether the semicircle bulges towards the resistance or away from it

The self inductance of a coil is L. Keeping the length and area same, the number of turns in the coil is increased to four times. The self inductance of the coil will now be 

(1) $\frac{1}{4}L$

(2) L

(3) 4 L

(4) 16 L