A straight wire carrying a current of 12 A is bent into a semi-circular arc of radius 2.0 cm as shown in the figure. Considering the magnetic field B at the centre of the arc, what will be the magnetic field due to the straight segments?

         

$1. 0$
$2. 1.2\times {10}^{-4} T$
$3. 2.1\times {10}^{-4} T$
$4. None of these$

An element \(\Delta l=\Delta x \hat{i}\) is placed at the origin and carries a large current of \(I=10\) A (as shown in the figure). What is the magnetic field on the y-axis at a distance of \(0.5\) m?(\(\Delta x=1~\mathrm{cm}\))
       

A long solenoid carrying a current produces a magnetic field \(B\) along its axis. If the current is doubled and the number of turns per cm is halved, what will be the new value of the magnetic field?
1. \(B/2\)
2. \(B\)
3. \(2B\)
4. \(4B\)

What properties will a galvanometer that is acting as a voltmeter have?

A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that $\overrightarrow{\mathrm{B}}$ is in the plane of the coil. If due to a current i in the triangle, a torque τ acts on it, the side l of the triangle will be:

1. $\frac{2}{\sqrt{3}}\left(\frac{\tau }{\mathrm{Bi}}\right)$ $$

2. $\frac{1}{\sqrt{3}}\frac{\tau }{\mathrm{Bi}}$

3. $2{\left(\frac{\tau }{\sqrt{3}\mathrm{Bi}}\right)}^{\frac{1}{2}}$

4. $\frac{2}{\sqrt{3}}{\left(\frac{\tau }{\mathrm{Bi}}\right)}^{\frac{1}{2}}$

A closely wound solenoid of 2000 turns and an area of cross-section of 1.5 × 10^–4 m² carries a current of 2.0 A. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field of 5 × 10^–2 Tesla, making an angle of 30^o with the axis of the solenoid. What will be the torque on the solenoid?

1. 1.5 × 10^–3 Nm

2. 1.5 × 10^–2 Nm

3. 3 × 10^–2 Nm

4. 3 × 10^–3 Nm

A galvanometer of resistance, \(\mathrm G,\) is shunted by the resistance of \(\mathrm S\) ohm. How much resistance is to be put in series with the galvanometer to keep the main current in the circuit unchanged?

A wire of length \(L\) meters carrying a current of \(I\) amp is bent in the form of a circle. What is its magnetic moment?
1. \( \frac{{IL}^2}{4} ~\text{A}\text-\text{m}^2 \)
2. \( \frac{{I} \times \pi {L}^2}{4} ~\text{A}\text-\text{m}^2 \)
3. \( \frac{2 {IL}^2}{\pi}~\text{A}\text-\text{m}^2 \)
4. \( \frac{{IL}^2}{4 \pi}~\text{A}\text-\text{m}^2 \)

Two identical current-carrying coaxial loops, carry current I in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as C,

Which of the above statements are correct?
1. a and b
2. a and c
3. b and c
4. c and d

A square loop with a side l is held in a uniform magnetic field B, such that its plane making an angle \(\alpha\)with B. A current I flows through the loop. What will be the torque experienced by the loop in this position?

1. ${\mathrm{Bil}}^2$

2. ${\mathrm{Bil}}^2\mathrm{sin\alpha }$

3. ${\mathrm{Bil}}^2\mathrm{cos\alpha }$

4. Zero