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

(i)	an equilateral triangle of side '\(a\)'
(ii)	a square of side '\(a\)'

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. \(-6\hat{i}-6\hat{j}-8\hat{k}\)

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 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.

The SI unit of magnetic field intensity is
1.  $Am{N}^{-1}$
2.  $N{A}^{-1}{m}^{-1}$
3.  $N{A}^{-2}{m}^{-2}$
4.  $N{A}^{-1}{m}^{-2}$

A solenoid has a core of material with relative permeability \(400.\) The windings of the solenoid are insulated from the core and carry a current of \(2~\text{A}.\) If the number of turns is \(1000\) per metre, the magnetizing current \(I_m\) is:
1. \(746~\text{A}\)
2. \(700~\text{A}\)
3. \(729~\text{A}\)
4. \(794~\text{A}\)

In the circuit (shown in the figure) the current is to be measured. What is the value of the current if the ammeter shown is a galvanometer $\left(R_G=60<mspace\; width="1em"></mspace>\Omega \right)$  but converted to an ammeter by a  shunt resistance $r_s=0.02<mspace\; width="1em"></mspace>\Omega$?

$1.<mspace\; width="1em"></mspace>0.99<mspace\; width="1em"></mspace>A$
$2.<mspace\; width="1em"></mspace>0.33<mspace\; width="1em"></mspace>A$
$3.<mspace\; width="1em"></mspace>0.26<mspace\; width="1em"></mspace>A$
$4.<mspace\; width="1em"></mspace>0.20<mspace\; width="1em"></mspace>A$

For the circuit (shown in the figure), the current is to be measured. The ammeter shown is a galvanometer with a resistance $R_G=60<mspace\; width="1em"></mspace>\Omega$. The value of current is:

1. 0.004 A

2. 0.032 A

3. 0.222 A

4. 0.048 A

Which one of the following statements is incorrect?

A 100 turn closely wound circular coil of radius 10 cm carries a current of 3.2 A. What is the angular speed acquired by the coil when it has rotated by 90° under the influence of a magnetic field of magnitude 2T that is applied along the axis of the coil? The moment of inertia of the coil is 0.1 kg-$m^2$.

$1.\mathrm{ 10}<mspace\; width="1em"></mspace>s^{-1}$
$2.\mathrm{ 30}<mspace\; width="1em"></mspace>s^{-1}$
$3.\mathrm{ 40}<mspace\; width="1em"></mspace>s^{-1}$
$4.\mathrm{ 20}<mspace\; width="1em"></mspace>s^{-1}$