A wheel with \(20\) metallic spokes, each \(1\) m long, is rotated with a speed of \(120\) rpm in a plane perpendicular to a magnetic field of \(0.4\) G. The induced emf between the axle and rim of the wheel will be:
\((1~\mathrm{G}=10^{-4}~\mathrm{T})\)
1. \(2.51 \times10^{-4}\) V
2. \(2.51 \times10^{-5}\) V
3. \(4.0 \times10^{-5}\) V
4. \(2.51\) V

A cycle wheel of radius \(0.5\) m is rotated with a constant angular velocity of \(10\) rad/s in a region of a magnetic field of \(0.1\) T which is perpendicular to the plane of the wheel. The EMF generated between its centre and the rim is:
1. \(0.25\) V
2. \(0.125\) V
3. \(0.5\) V
4. zero

A conducting square frame of side \(a\) and a long straight wire carrying current \(I\) are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity \(v.\) The emf induced in the frame will be proportional to:

     
1. \( \frac{1}{x^2} \)
2. \( \frac{1}{(2 x-a)^2} \)
3. \( \frac{1}{(2 x+a)^2} \)
4. \(\frac{1}{(2 x-a)(2 x+a)}\)

A thin semicircular conducting the ring \((PQR)\) of radius \(r\) is falling with its plane vertical in a horizontal magnetic field \(B,\) as shown in the figure. The potential difference developed across the ring when it moves with speed \(v\) is: 

     

A rectangular, a square, a circular, and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity, $\overrightarrow{\mathrm{v}}=\mathrm{v}\hat{\mathrm{i}}$. The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops out of the field region, will not remain constant for:

Initially plane of a coil is parallel to the uniform magnetic field B. If in time ∆t the coil is perpendicular to the magnetic field, then charge flows in ∆t depends on this time as:

1. $\propto$ $∆t$

2. $\propto$ $\frac{1}{∆t}$

3. $\propto$ ${(∆t)}^0$

4. $\propto$ ${(∆t)}^2$