A cylindrical conductor of radius \(R\) is carrying a constant current. The plot of the magnitude of the magnetic field \(B\) with the distance \(d\) from the centre of the conductor is correctly represented by the figure:

1.		2.
3.		4.

Two toroids \(1\) and \(2\) have total no. of turns \(200\) and \(100\) respectively with average radii \(40~\text{cm}\) and \(20~\text{cm}\) respectively. If they carry the same current \(i,\) what will be the ratio of the magnetic fields along the two loops?
1. \(1:1\)
2. \(4:1\)
3. \(2:1\)
4. \(1:2\)

A long solenoid of \(50~\text{cm}\) length having \(100\) turns carries a current of \(2.5~\text{A}\). The magnetic field at the centre of the solenoid is: 
\(\big(\mu_0 = 4\pi\times 10^{-7}~\text{TmA}^{-1} \big)\)
1. \(3.4\times 10^{-4}~\text{T}\)
2. \(6.28\times 10^{-5}~\text{T}\)
3. \(3.14\times 10^{-5}~\text{T}\)
4. \(6.28\times 10^{-4}~\text{T}\)

A thick current-carrying cable of radius '\(R\)' carries current \('I'\) uniformly distributed across its cross-section. The variation of magnetic field \(B(r)\) due to the cable with the distance '\(r\)' from the axis of the cable is represented by:

1.		2.
3.		4.

An infinitely long straight conductor carries a current of \(5~\text{A}\) as shown. An electron is moving with a speed of ${\mathrm{}}^{}$\(10^5~\text{m/s}\) parallel to the conductor. The perpendicular distance between the electron and the conductor is \(20~\text{cm}\) at an instant. Calculate the magnitude of the force experienced by the electron at that instant.

1. \(4\pi\times 10^{-20}~\text{N}\)
2. \(8\times 10^{-20}~\text{N}\)
3. \(4\times 10^{-20}~\text{N}\)
4. \(8\pi\times 10^{-20}~\text{N}\)

A uniform conducting wire of length \(12a\) and resistance '\(R\)' is wound up as a current-carrying coil in the shape of;

The magnetic dipole moments of the coil in each case respectively are:
1. \(3Ia^2~\text{and}~4Ia^2\)
2. \(4Ia^2~\text{and}~3Ia^2\)
3. \(\sqrt{3}Ia^2~\text{and}~3Ia^2\)
4. \(3Ia^2~\text{and}~Ia^2\)

In the product 
\(\vec{F}=q\left ( \vec{v}\times \vec{B} \right )=q\vec{v}\times \left ( B\hat{i}+B\hat{j}+B_0\hat{k} \right ).\) For \(q=1 \) and \(\vec{v}=2\hat{i}+4\hat{j}+6\hat{k} \)  and \(\vec{F}=4\hat{i}-20\hat{j}+12\hat{k},\) what will be the complete expression for \(\vec{B} \)?
1. \(8\hat{i}+8\hat{j}-6\hat{k}\)
2. \(6\hat{i}+6\hat{j}-8\hat{k}\)
3. \(-8\hat{i}-8\hat{j}-6\hat{k}\)
4. \(-6\hat{i}-6\hat{j}-8\hat{k}\)