An emf is generated by an ac generator having \(100\) turn coil, of loop area \(1\) m². The coil rotates at a speed of one revolution per second and placed in a uniform magnetic field of \(0.05\) T perpendicular to the axis of rotation of the coil. The maximum value of emf is:
1. \(3.14\) V
2. \(31.4\) V
3. \(62.8\) V
4. \(6.28\) V

An inductor coil of self-inductance \(10~\mathrm H\) carries a current of \(1~\mathrm A\) . The magnetic field energy stored in the coil is:

The dimensions of mutual inductance \((M)\) are:
1. \(\left[M^2LT^{-2}A^{-2}\right]\)
2. \(\left[MLT^{-2}A^{2}\right]\)
3. \(\left[M^{2}L^{2}T^{-2}A^{2}\right]\)
4. \(\left[ML^{2}T^{-2}A^{-2}\right]\)

The current in an inductor of self-inductance \(4~\text{H}\) changes from \(4~ \text{A}\) to \(2~\text{A}\) in \(1~ \text s\). The emf induced in the coil is:
1. \(-2~\text{V}\)
2. \(2~\text{V}\)
3. \(-4~\text{V}\)
4. \(8~\text{V}\)

Kamla peddles a stationary bicycle. The pedals of the bicycle are attached to a \(100\) turn coil of an area of \(0.10~\text{m}^2\). The coil rotates at half a revolution per second and it is placed in a uniform magnetic field of \(0.01~\text{T}\) perpendicular to the axis of rotation of the coil. What is the maximum voltage generated in the coil?
1. \(0.628~\text{V}\)
2. \(0.421~\text{V}\)
3. \(0.314~\text{V}\)
4. \(0\) 

The ratio of magnetic energy per unit volume and electrostatic energy stored per unit volume in a parallel plate capacitor is:

$1. \frac{1}{{\mathrm{\epsilon }}_0{\mathrm{\mu }}_0}{\left(\frac{\mathrm{B}}{\mathrm{E}}\right)}^2$
$2. \frac{1}{{\mathrm{\epsilon }}_0{\mathrm{\mu }}_0}{\left(\frac{\mathrm{E}}{\mathrm{B}}\right)}^2$
$3. \frac{1}{2{\mathrm{\epsilon }}_0{\mathrm{\mu }}_0}{\left(\frac{\mathrm{B}}{\mathrm{E}}\right)}^2$
$4. \frac{1}{2{\mathrm{\epsilon }}_0{\mathrm{\mu }}_0}{\left(\frac{\mathrm{E}}{\mathrm{B}}\right)}^2$