Q. No.The expression for the magnetic energy stored in a solenoid in terms of magnetic field \(B\), area \(A\) and length \(l\) of the solenoid is:
1.
\( \dfrac{1}{\mu_0}B^2Al\)
2.
\( \dfrac{1}{2\mu_0}B^2Al\)
3.
\( \dfrac{2}{\mu_0}B^2Al\)
4.
\( \dfrac{3}{2\mu_0}B^2Al\)
Two concentric circular coils, one of small radius \({r_1}\) and the other of large radius \({r_2},\) such that \({r_1<<r_2},\) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is:
1. \(\dfrac{\mu_0\pi r_1^2}{3r_2}\)
2. \(\dfrac{2\mu_0\pi r_1^2}{r_2}\)
3. \(\dfrac{\mu_0\pi r_1^2}{r_2}\)
4. \(\dfrac{\mu_0\pi r_1^2}{2r_2}\)
A wheel with \(10\) metallic spokes each \(0.5~\text{m}\) long is rotated with a speed of \(120~\text{rev/min}\) in a plane normal to the horizontal component of Earth’s magnetic field \(H_E\) at a place. If \(H_E=0.4~\text{G}\) at the place, what is the induced emf between the axle and the rim of the wheel? (\((1~\text{G}=10^{-4}~\text{T})\)
1. \(5.12\times10^{-5}~\text{V}\)
2. \(0\)
3. \(3.33\times10^{-5}~\text{V}\)
4. \(6.28\times10^{-5}~\text{V}\)
The figure shows planar loops of different shapes moving out of or into a region of a magnetic field which is directed normally to the plane of the loop away from the reader. Then:
| 1. | for the rectangular loop \(abcd,\) the induced current is clockwise. |
| 2. | for the triangular loop \(abc,\) the induced current is clockwise. |
| 3. | for the irregularly shaped loop \(abcd,\) the induced current is anti-clockwise. |
| 4. | none of these. |
In a coil of resistance \(10\) \(\Omega\), the induced current developed by changing magnetic flux through it is shown in the figure as a function of time. The magnitude of change in flux through the coil in Weber is:
1. \(2\)
2. \(6\)
3. \(4\)
4. \(8\)
A rod of length \(l\) rotates with a uniform angular velocity \(\omega\) about its perpendicular bisector. A uniform magnetic field \(B\) exists parallel to the axis of rotation. The potential difference between the two ends of the rod is:
1. zero
2. \(\frac{1}{2}Bl\omega ^{2}\)
3. \(Bl\omega ^{2}\)
4. \(2Bl\omega ^{2}\)
A conducting rod is moved with a constant velocity \(v\) in a magnetic field. A potential difference appears across the two ends:
| (a) | if \(\overrightarrow v \|\overrightarrow l\) | (b) | if \(\overrightarrow v \|\overrightarrow B\) |
| (c) | if \(\overrightarrow l \|\overrightarrow B\) | (d) | none of these |
Choose the correct option from the given ones:
| 1. | (a) and (b) only |
| 2. | (b) and (c) only |
| 3. | (d) only |
| 4. | (a) and (d) only |
| 1. | \(vBl\) | 2. | \(\dfrac{vBl}{2}\) |
| 3. | \(\dfrac{\sqrt 3}{2}vBl\) | 4. | \(\dfrac{1}{\sqrt 3}vBl\) |
1. \(2\times10^{-6} \) T
2. \(4\times10^{-6} \) T
3. \(2\times10^{-3} \) T
4. \(4\times10^{-3} \) T
| 1. | \((\cos \alpha+\sin \alpha) \dfrac{d B}{d t}\) |
| 2. | \( (\cos \alpha-\sin \alpha) \dfrac{d B}{d t}\) |
| 3. | \((\tan \alpha+\cot \alpha) \dfrac{d B}{d t}\) |
| 4. | \( (\tan \alpha-\cot \alpha) \dfrac{dB}{d t}\) |
© 2025 GoodEd Technologies Pvt. Ltd.