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 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

The primary and secondary coils of a transformer have \(50\) and \(1500\) turns respectively. If the magnetic flux \(\phi\) linked with the primary coil is given by \(\phi=\phi_0+4t,\) where \(\phi\) is in Weber, \(t\) is time in seconds, and \(\phi_0\)  is a constant, the output voltage across the secondary coil is:
1. \(90~\mathrm{V}\)
2. \(120~\mathrm{V}\)
3. \(220~\mathrm{V}\)
4. \(30~\mathrm{V}\)

The sun delivers ${10}^3 w/m^2$ 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) $2.56\times {10}^4 W$             (2) $6.4\times {10}^5 W$

(3) $4.0\times {10}^5 W$                (4) $1.6\times {10}^5 W$

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

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

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