A conducting circular loop is placed in a uniform magnetic field, \(B=0.025~\text{T}\) with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1~\text{mm s}^{-1}\). The induced emf, when the radius is \(2~\text{cm}\), is:
1. \(2\pi ~\mu\text{V}\)
2. \(\pi ~\mu\text{V}\)
3. \(\dfrac{\pi}{2}~\mu\text{V}\)
4. \(2 ~\mu \text{V}\)
The current \((I)\) in the inductance is varying with time \((t)\) according to the plot shown in the figure.
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A coil of resistance \(400~\Omega\) is placed in a magnetic field. The magnetic flux \(\phi~\text{(Wb)}\) linked with the coil varies with time \(t~\text{(s)}\) as \(\phi=50t^{2}+4.\) The current in the coil at \(t=2~\text{s}\) is:
1. \(0.5~\text{A}\)
2. \(0.1~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)
1. | twice per revolution. |
2. | four times per revolution. |
3. | six times per revolution. |
4. | once per revolution. |
The magnetic potential energy stored in a certain inductor is \(25~\text{mJ},\) when the current in the inductor is \(60~\text{mA}.\) This inductor is of inductance:
1. \(0.138~\text H\)
2. \(138.88~\text H\)
3. \(1.389~\text H\)
4. \(13.89~\text H\)
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. \(8\)
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. | \( \dfrac{3}{2\mu_0}B^2Al\) |