If the instantaneous charge in the capacitor is 400$\mu$C and current through the circuit is decreasing at the rate 10³ A/s, then potential difference V_A-V_B is equal to

1. 30 V

2. Zero

3. 10 V

4. 70 V

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

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

         
1. \(20~\text{ms}\)
2. \(0.02~\text{ms}\)
3. \(2~\text{ms}\)
4. \(0.2~\text{ms}\)

A coil of resistance \(400~\Omega\) is placed in a magnetic field. The magnetic flux \(\phi~\text{(Wb)}\) linked with the coil varies with time \(t~\text{(s)}\) as \(\phi=50t^{2}+4.\) The current in the coil at \(t=2~\text{s}\) is:$$
1. \(0.5~\text{A}\)
2. \(0.1~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)

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? 
                       

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 the area $7 {\mathrm{cm}}^2$ and of 50 turns is kept with its plane normal to a magnetic field B. A resistance of 30 ohms is connected to the resistance-less coil. B is $75{\mathrm{e}}^{-200\mathrm{t}}$ 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.  $2.60 \mathrm{mA}$

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.  $40 \mathrm{\mu V}$