A circular loop of radius R carrying current I lies in the x-y plane with its centre at the origin. The total magnetic flux through the x-y plane is 

1. Directly proportional to I

2. Directly proportional to R

3. Directly proportional to R²

4. Zero

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. \(0.01~\text{Wb}\)

The sun delivers ${10}^3<mspace\; width="1em"></mspace>w/m^2$ of electromagnetic flux to the earth's surface.  The total power that is incident on a roof of dimensions 8 m$\times$20 m will be

(1) $2.56\times {10}^4<mspace\; width="1em"></mspace>W$             (2) $6.4\times {10}^5<mspace\; width="1em"></mspace>W$

(3) $4.0\times {10}^5<mspace\; width="1em"></mspace>W$                (4) $1.6\times {10}^5<mspace\; width="1em"></mspace>W$

The magnetic flux linked with a coil (in Wb) is given by the equation 

$\varphi =5t^2+3t+16$

The magnitude of induced emf in the coil at the four-second will be

(1) 33 V

(2) 43 V

(3) 108 V

(4) 10 V

If a loop changes from an irregular shape to a circular shape, then magnetic flux linked with it:
1. decreases
2. remains constant
3. first decreases and then increases
4. increases

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. \(\sqrt{29} B_{0} L^{2}~\text{Wb}\)$$

A loop, made of straight edges has six corners at A(0, 0, 0), B(L, 0, 0), C(L, L, 0), D(0, L, 0), E(0, L, L) and F(0, 0, L). A magnetic field B=${\mathrm{B}}_0\left(\hat{\mathrm{i}}+\hat{\mathrm{k}}\right)$ T is present in the region. The flux passing through the loop ABCDEFA (in that order) is:

1. B₀L² Wb³ 

2. 2B₀L² Wb

3. \(\sqrt2\)B₀L² Wb

4. 4B₀L² Wb