Q. No.A conducting square loop of side \(L\) and resistance \(R\) moves in its plane with a uniform velocity \(v\) perpendicular to one of its sides. A magnetic induction \(B\) constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere. The current induced in the loop is:
1.
\(\dfrac{Blv}{R}\) clockwise
2.
\(\dfrac{Blv}{R}\) anticlockwise
3.
\(\dfrac{2Blv}{R}\) anticlockwise
4.
zero
A thin semicircular conducting ring of radius \(R\) is falling with its plane vertical in a horizontal magnetic induction \(B\). At the position \(MNQ\), the speed of the ring is \(v\) and the potential difference developed across the ring is:
| 1. | Zero |
| 2. | \(B v \pi R^2 / 2\) and \(M\) is at the higher potential |
| 3. | \(2 R B v\) and \(M\) is at the higher potential |
| 4. | \(2RBv\) and \(Q\) is at the higher potential |
A conducting wireframe is placed in a magnetic field that is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires \(AB\) and \(CD\) are:
| 1. | \(B\) to \(A\) and \(D\) to \(C\) |
| 2. | \(A\) to \(B\) and \(C\) to \(D\) |
| 3. | \(A\) to \(B\) and \(D\) to \(C\) |
| 4. | \(B\) to \(A\) and \(C\) to \(D\) |
A square metallic wire loop of side \(0.1~\text m\) and resistance of \(1~\Omega\) is moved with a constant velocity in a magnetic field of \(2~\text{wb/m}^2\) as shown in the figure. The magnetic field is perpendicular to the plane of the loop and the loop is connected to a network of resistances. What should be the velocity of the loop so as to have a steady current of \(1~\text{mA}\) in the loop?
1. \(1~\text{cm/s}\)
2. \(2~\text{cm/s}\)
3. \(3~\text{cm/s}\)
4. \(4~\text{cm/s}\)
The resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is \(10~\Omega.\) The current in the circuit will be:
| 1. | \(i = 0.5~\text{A}\) | 2. | \(i > 0.5~\text{A}\) |
| 3. | \(i < 0.5~\text{A}\) | 4. | \(i = 0\) |
A rectangular loop with a sliding connector of length \(l= 1.0\) m is situated in a uniform magnetic field \(B = 2T\) perpendicular to the plane of the loop. Resistance of connector is \(r=2~\Omega\). Two resistances of \(6~\Omega\) and \(3~\Omega\) are connected as shown in the figure. The external force required to keep the connector moving with a constant velocity \(v = 2\) m/s is:
1. \(6~\text{N}\)
2. \(4~\text{N}\)
3. \(2~\text{N}\)
4. \(1~\text{N}\)
The figure shows three circuits with identical batteries, inductors, and resistors. Rank the circuits according to the current, in descending order, through the battery \((i)\) just after the switch is closed and \((ii)\) a long time later:
| 1. | \((i)~ i_2>i_3>i_1\left(i_1=0\right) (ii) ~i_2>i_3>i_1\) |
| 2. | \((i)~ i_2<i_3<i_1\left(i_1 \neq 0\right) (ii)~ i_2>i_3>i_1\) |
| 3. | \((i) ~i_2=i_3=i_1\left(i_1=0\right) (ii)~ i_2<i_3<i_1\) |
| 4. | \((i)~ i_2=i_3>i_1\left(i_1 \neq 0\right) (ii) ~i_2>i_3>i_1\) |
Switch \(S\) of the circuit shown in the figure is closed at \(t=0\). If \(e\) denotes the induced emf in \(L\) and \(i\) denotes the current flowing through the circuit at time \(t\), then which of the following graphs is correct?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
An electron moves on a straight-line path \(XY\) as shown. The \(abcd\) is a coil adjacent to the path of the electron. What will be the direction of the 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 is induced. |
A circular disc of the radius \(0.2~\text m\) is placed in a uniform magnetic field of induction \(\dfrac{1}{\pi} \left(\dfrac{\text{Wb}}{\text{m}^{2}}\right)\) in such a way that its axis makes an angle of \(60^{\circ}\) with \(\vec {B}.\) The magnetic flux linked to the disc will be:
1. \(0.02~\text{Wb}\)
2. \(0.06~\text{Wb}\)
3. \(0.08~\text{Wb}\)
4. \(0.01~\text{Wb}\)
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