A circular disc of radius 0.2 m is placed in a uniform magnetic field of induction $\frac{1}{\pi }$ $\left(\frac{Wb}{m^2}\right)$ in such a way that its axis makes an angle of ${60}^{°}$ with $\overrightarrow{B}$. 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. $\frac{{\mu }_{0}I{l}^2}{2R}$

3. $\frac{{\mu }_{0}l{\mathrm{\pi R}}^2}{2l}$

4. $\frac{{\mu }_0{\mathrm{\pi R}}^{2}I}{l}$

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

What is the dimensional formula of magnetic flux?

1. $[\mathrm{M}$ ${\mathrm{L}}^2$ ${\mathrm{T}}^{-2}$ ${\mathrm{A}}^{-1}]$

2. $[\mathrm{M}$ ${\mathrm{L}}^1$ ${\mathrm{T}}^{-1}$ ${\mathrm{A}}^{-2}]$

3. $[\mathrm{M}$ ${\mathrm{L}}^2$ ${\mathrm{T}}^{-3}$ ${\mathrm{A}}^{-1}]$

4. $[\mathrm{M}$ ${\mathrm{L}}^{-2}$ ${\mathrm{T}}^{-2}$ ${\mathrm{A}}^{-2}]$

The magnetic flux linked with a coil varies with time as $\varphi$ $=$ $2t^2-6t+5$, where $\varphi$ is in weber and t is in seconds. The induced current is zero at:

1. t = 0

2. t = 1.5 s

3. t = 3 s

4. t = 5 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 $\mathrm{\omega }$. The maximum value of the emf induced in it is:

1. $\frac{\mathrm{NBA}}{\mathrm{\omega }}$                             

2. $\mathrm{NBA\omega }$

3. $\frac{\mathrm{NBA}}{{\mathrm{\omega }}^2}$                             

4. ${\mathrm{NBA\omega }}^2$

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

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

A coil having an area $A_0$ is placed in a magnetic field which changes from $B_0$ $to$ $4B_0$ in time interval t. The average EMF induced in the coil will be:

1. $\frac{3A_0{B}_0}{t}$

2. $\frac{4A_0{B}_0}{t}$

3. $\frac{3B_0}{A_{0}t}$

4. $\frac{4B_0}{A_{0}t}$

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