The net magnetic flux through any closed surface, kept in uniform magnetic field is:

A circular disc of the radius $0.2~\text m$ is placed in a uniform magnetic field of induction $\dfrac{1}{\pi} \left(\dfrac{\text{Wb}}{\text{m}^{2}}\right)$ 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. $0.02~\text{Wb}$
2. $0.06~\text{Wb}$
3. $0.08~\text{Wb}$
4. $0.01~\text{Wb}$

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. $\dfrac{\mu_{0} I}{2} \dfrac{R^{2}}{l}$
2. $\dfrac{\mu_{0} I l^{2}}{2 R}$
3. $\dfrac{\mu_{0}I \pi R^{2}}{2 l}$
4. $\dfrac{\mu_{0} \pi R^{2} I}{l}$

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:
            
1. $2 \pi \times 10^{-2}~\text{Wb}$
2. $3 \pi \times 10^{-4}~\text{Wb}$
3. $5 \pi \times 10^{-5}~\text{Wb}$
4. $5 \pi \times 10^{-4}~\text{Wb}$

A square of side $L$ meters lies in the $XY\text-$plane in a region where the magnetic field is given by $\vec{B}=B_{0}\left ( 2\hat{i} +3\hat{j}+4\hat{k}\right )\text{T}$ where $B_{0}$ is constant. The magnitude of flux passing through the square will be:
1. $2 B_{0} L^{2}~\text{Wb}$
2. $3 B_{0} L^{2}~\text{Wb}$
3. $4 B_{0} L^{2}~\text{Wb}$
4. $\sqrt{29} B_{0} L^{2}~\text{Wb}$

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:

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. $NBAω^{2}$