A circular disc of radius \(0.2\) m is placed in a uniform magnetic field of induction \(\frac{1}{\pi} \left(\frac{\text{Wb}}{\text{m}^{2}}\right)\)
in such a way that its axis makes an angle of \(60^{\circ}\) with \(\vec {B}.\) The magnetic flux linked to the disc will be:
1. \(0.02\) Wb
2. \(0.06\) Wb
3. \(0.08\) Wb
4. \(0.01\) Wb

If a current is passed through a circular loop of radius \(R\) then magnetic flux through a coplanar square loop of side \(l\) as shown in the figure \((l<<R)\) is:

1. \(\frac{\mu_{0} l}{2} \frac{R^{2}}{l}\)

2. \(\frac{\mu_{0} I l^{2}}{2 R}\)

3. \(\frac{\mu_{0} l \pi R^{2}}{2 l}\)

4. \(\frac{\mu_{0} \pi R^{2} I}{l}\)

The radius of a loop as shown in the figure is \(10~\text{cm}.\) If the magnetic field is uniform and has a value \(10^{-2}~ \text{T},\) then the flux through the loop will be:
 

What is the dimensional formula of magnetic flux?
1. \(\left[ M L^2 T^{-2}A^{-1}\right]\)
2. \(\left[ M L^1 T^{-1}A^{-2}\right]\)
3. \(\left[ M L^2 T^{-3}A^{-1}\right]\)
4. \(\left[ M L^{-2} T^{-2}A^{-2}\right]\)$$

The magnetic flux linked with a coil varies with time as \(\phi = 2t^2-6t+5,\) where \(\phi \) is in Weber and \(t\) is in seconds. The induced current is zero at:
1. \(t=0\)
2. \(t= 1.5~\text{s}\)
3. \(t=3~\text{s}\)
4. \(t=5~\text{s}\)

A coil having number of turns \(N\) and cross-sectional area \(A\) is rotated in a uniform magnetic field \(B\) with an angular velocity \(\omega\). The maximum value of the emf induced in it is:
1. \(\frac{NBA}{\omega}\)
2. \(NBAω\)
3. \(\frac{NBA}{\omega^{2}}\)
4. \(NBAω^{2}\)

The current in a coil varies with time \(t\) as \(I= 3 t^{2} +2t\). If the inductance of coil be \(10\) mH, the value of induced emf at \(t=2~\text{s}\) will be:
1. \(0.14~\text{V}\)
2. \(0.12~\text{V}\)
3. \(0.11~\text{V}\)
4. \(0.13~\text{V}\)

A bar magnet is released along the vertical axis of the conducting coil. The acceleration of the bar magnet is:

A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced e.m.f. is: