A square wire loop of 10.0 cm side lies at right angles to a uniform magnetic field of 20T. A 10 V light bulb is in series with the loop as shown in the fig. The magnetic field is decreasing steadily to zero over a time interval $∆$t. The bulb will shine with full brightness if $∆$t is equal to

1. 20 ms

2. 0.02 ms

3. 2 ms

4. 0.2 ms

The magnetic flux through a stationary loop with resistance R varies during the interval of time T as $\mathrm{\varphi }$ = at(T - t). The heat generated during this time neglecting the inductance of loop will be

$1. \frac{{\mathrm{a}}^2{\mathrm{T}}^3}{3\mathrm{R}}$
$2. \frac{{\mathrm{a}}^2{\mathrm{T}}^2}{3\mathrm{R}}$
$3. \frac{{\mathrm{a}}^2\mathrm{T}}{3\mathrm{R}}$
$4. \frac{{\mathrm{a}}^2{\mathrm{T}}^3}{\mathrm{R}}$

A thin semicircular conducting the ring (PQR) of radius 'r' is falling with its plane vertical in a horizontal magnetic field B, as shown in figure. The potential difference developed across the ring when its speed is v is: 

1. Zero

2. $Bv{\mathrm{\pi r}}^2/2$ and P is at the higher potential

3. $\mathrm{\pi rBv}$ and R is at the higher potential

4. 2BvR and R is at the higher potential

An electron moves on a straight-line path XY as shown. The abcd is a coil adjacent to the path of electrons. What will be the direction of current if any, induced in the coil? 

1. abcd

2. adcb

3. The current will reverse its direction as the electron goes past the coil

4. No current included

A long solenoid has \(1000\) turns. When a current of \(4\) A flows through it, the magnetic flux linked with each turn of the solenoid is \(4\times 10^{-3}\) Wb. The self-inductance of the solenoid is:
1. \(3\) H
2. \(2\) H
3. \(1\) H
4. \(4\) H

Assertion: The magnetic flux linked with a coil is $\mathrm{\varphi }$, and the emf induced in it is $\mathrm{\epsilon }$. If $\mathrm{\varphi }=0$, $\mathrm{\epsilon }$ must be zero.

Reason : $\mathrm{\epsilon }=\frac{-\mathrm{d\varphi }}{\mathrm{dt}} \Rightarrow \mathrm{\epsilon }=0 \mathrm{when} \mathrm{\varphi }=0$

(a) Assertion and Reason both are correct and the Reason is the correct explanation of the Assertion.

(b) Assertion and Reason both are correct but the Reason is not the correct explanation of the Assertion.

(c) The assertion is correct but the Reason is wrong.

(d) Assertion and Reason both are wrong.

A coil of area $7 {\mathrm{cm}}^2$ and of 50 turns is kept with its plane normal to a magnetic field B. A resistance of 30 ohm is connected to the resistance-less coil. B is 75 exp (– 200t) gauss. The current passing through the resistance at t = 5 ms will be-

1.  $0.64 \mathrm{mA}$                     

2.  $1.05 \mathrm{mA}$ 

3.  $1.75 \mathrm{mA}$                     

4.  $14 2.60 \mathrm{mA}$

A long solenoid having 1000 turns per cm is carrying alternating current of one ampere peak value. A search coil of area of cross-section $1\times {10}^{-4} {\mathrm{m}}^2$ and of 20 turns is placed in the middle of the solenoid so that its plane is perpendicular to the axis of the solenoid. The search coil registers a peak voltage $2.5\times {10}^{-2} \mathrm{V}$. The frequency of the current in the solenoid is -

1.  1.6 per second                   

2.  0.16 per second

3.  15.9 per second                 

4.  15.85 per second

A copper rod of length 0.19 m is moving parallel to a long wire with a uniform velocity of 10 m/s. The long wire carries 5 ampere current and is perpendicular to the rod. The ends of the rod are at distances 0.01 m and 0.2 m from the wire. The emf induced in the rod will be-

1.  $10 \mathrm{\mu V}$                           

2.  $20 \mathrm{\mu V}$

3.  $30 \mathrm{\mu V}$                           

4.  $40 \mathrm{\mu V}$

An emf of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time t = $\infty$ and at t = 1 second is -

1.  $\frac{{\mathrm{e}}^{1/2}}{{\mathrm{e}}^{1/2}-1}$                               

2.  $\frac{{\mathrm{e}}^2}{{\mathrm{e}}^2-1}$

3.  $1-{\mathrm{e}}^{-1}$                           

4.  ${\mathrm{e}}^{-1}$