Q. No.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.
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. \(6.28\times10^{-5}~\text{V}\)
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. \(\dfrac{\mu_0\pi r_1^2}{2r_2}\)
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. | \( \dfrac{3}{2\mu_0}B^2Al\) |
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. | \( (\tan \alpha-\cot \alpha) \dfrac{dB}{d t}\) |
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