The net magnetic flux through any closed surface, kept in uniform magnetic field is:
1. zero
2. \(\frac{\mu_{0}}{4 \pi}\)
3. \(4\pi μ_{0}\)
4. \(\frac{4\mu_{0}}{\pi}\)

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

A square of side L meters lies in the XY-plane in a region where the magnetic field is given by \(\vec{B}=B_{0}\left ( 2\hat{i} +3\hat{j}+4\hat{k}\right )~T\) where \(B_{0}\) is constant. The magnitude of flux passing through the square will be:

1. $2{\mathrm{B}}_0{\mathrm{L}}^2 \mathrm{Wb}$
2. $3{\mathrm{B}}_0{\mathrm{L}}^2 \mathrm{Wb}$
3. $4{\mathrm{B}}_0{\mathrm{L}}^2 \mathrm{Wb}$
4. $\sqrt{29}{\mathrm{B}}_0{\mathrm{L}}^2 \mathrm{Wb}$

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

A circular loop of radius R carrying current i lies in the x-y plane. If the centre of the loop coincides with the origin, then the total magnetic flux passing through the x-y plane will be:

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