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