Q. No.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. \(8\)
2. \(6\)
3. \(4\)
4. \(8\)
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 \(0.5\) m long is rotated with a speed of \(120\) rev/min in a plane normal to the horizontal component of earth’s magnetic field HE at a place. If \(H_E=0.4\) G at the place, what is the induced emf between the axle and the rim of the wheel? (\(1\) G=\(10^{-4}\) T)
1. \(5.12\times10^{-5}\) T
2. \(0\)
3. \(3.33\times10^{-5}\)
4. \(6.28\times10^{-5}\)
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. \(\frac{\mu_0\pi r_1^2}{3r_2}\)
2. \(\frac{2\mu_0\pi r_1^2}{r_2}\)
3. \(\frac{\mu_0\pi r_1^2}{r_2}\)
4. \(\frac{\mu_0\pi r_1^2}{2r_2}\)
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. \( \frac{1}{\mu_0}B^2Al\)
2. \( \frac{1}{2\mu_0}B^2Al\)
3. \( \frac{2}{\mu_0}B^2Al\)
4. \( \frac{3}{2\mu_0}B^2Al\)
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:
| 1. | (a), (b) | 2. | (b), (c) |
| 3. | (d) only | 4. | (a), (d) |
| 1. | \(vBl\) | 2. | \(vBl \over 2\) |
| 3. | \({\sqrt 3 \over 2}vBl\) | 4. | \({1 \over \sqrt 3}vBl\) |
1. \(2\times10^{-6} \) T
2. \(4\times10^{-6} \) T
3. \(2\times10^{-3} \) T
4. \(4\times10^{-3} \) T
\(1.~ (\cos \alpha+\sin \alpha) \frac{d B}{d t}\\ 2.~ (\cos \alpha-\sin \alpha) \frac{d B}{d t}\\ 3.~ (\tan \alpha+\cot \alpha) \frac{d B}{d t}\\ 4.~ (\tan \alpha-\cot \alpha) \frac{dB}{d t}\)
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