Q. No.A wooden stick of length is rotated about an end with constant angular velocity in a uniform magnetic field B perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the potential difference across the whole length of the stick is –
1.
2.
3.
4.
A wheel with \(20\) metallic spokes, each \(1\) m long, is rotated with a speed of \(120\) rpm in a plane perpendicular to a magnetic field of \(0.4~\text{G}\). The induced emf between the axle and rim of the wheel will be:
\((1~\text{G}=10^{-4}~\text{T})\)
1. \(2.51 \times10^{-4}\) V
2. \(2.51 \times10^{-5}\) V
3. \(4.0 \times10^{-5}\) V
4. \(2.51\) V
A cycle wheel of radius \(0.5\) m is rotated with a constant angular velocity of \(10\) rad/s in a region of a magnetic field of \(0.1\) T which is perpendicular to the plane of the wheel. The EMF generated between its centre and the rim is:
| 1. | \(0.25\) V | 2. | \(0.125\) V |
| 3. | \(0.5\) V | 4. | zero |
1. \(3.14\) V
2. \(31.4\) V
3. \(62.8\) V
4. \(6.28\) V
A conducting square frame of side \(a\) and a long straight wire carrying current \(I\) are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity \(v.\) The emf induced in the frame will be proportional to:
| 1. | \( \dfrac{1}{x^2} \) | 2. | \( \dfrac{1}{(2 x-a)^2} \) |
| 3. | \( \dfrac{1}{(2 x+a)^2} \) | 4. | \(\dfrac{1}{(2 x-a)(2 x+a)}\) |
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 the figure. The potential difference developed across the ring when it moves with speed \(v\) is:
| 1. | zero |
| 2. | \(Bv\pi r^{2}/2\) and \(P\) is at a higher potential |
| 3. | \(\pi rvB\) and \(R\) is at a higher potential |
| 4. | \(2BvR\) and \(R\) is at a higher potential |
Rings are rotated and translated in a uniform magnetic field as shown in the figure. Arrange the magnitude of emf induced across \(AB\):
| 1. | \(\mathrm{emf_{a}<emf_{b}<emf_{c}}\) |
| 2. | \(\mathrm{emf_{a}=emf_{b}<emf_{c}}\) |
| 3. | \(\mathrm{emf_{a}={emf}_{c}<{emf}_{b}}\) |
| 4. | \(\mathrm{emf_{a}<emf_{b}={emf}_{c}}\) |
| 1. | \(1~\text V\) | 2. | \(2~\text V\) |
| 3. | \(1.5~\text V\) | 4. | \(\dfrac43~\text V\) |
| Assertion (A): | The average induced electric field within the wire has a magnitude of \(\dfrac12B\omega L.\) |
| Reason (R): | The induced electric field is the motional EMF per unit length, and the motional EMF is \(\dfrac12B\omega L^2.\) |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
1. \(6\) V
2. \(3\) V
3. \(1\) V
4. \(5\) V
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