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. Consider the magnetic field B at the centre of the arc. What is the magnetic field at centre due to the semi-circular loop?

 

$1. 0$
$2. 3.8\times {10}^{-4} T$
$3. 1.9\times {10}^{-4} T$
$4. 2.9\times {10}^{-4} T$

Consider a tightly wound \(100\) turn coil of radius \(10\) cm, carrying a current of \(1\) A. What is the magnitude of the magnetic field at the centre of the coil?
1. \(8.2\times10^{-4}\) T
2. \(4.6\times10^{-4}\) T
3. \(5.2\times10^{-4}\) T
4. \(6.2\times10^{-4}\) T

The figure shows a long straight wire of a circular cross-section (radius a) carrying steady current I. The current I is uniformly distributed across this cross-section. If the magnetic field in the region (r < a) is $B_1$ and for (r > a) is $B_2$, then $\frac{B_1}{B_2}$ is:

$1. \frac{a}{r}$
$2. \frac{a^2}{r^2}$
$3. \frac{r^2}{a^2}$
$4. \frac{r}{a}$

A solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns. It carries a current of 5 A. What is the magnitude of the magnetic field inside the solenoid?

$1. 6.28\times {10}^{-3} T$
$2. 3.14\times {10}^{-3} T$
$3. 2.72\times {10}^{-3} T$
$4. 5.17\times {10}^{-3} T$

The horizontal component of the earth’s magnetic field at a certain place is \(3.0\times10^{-5}~\text{T}\) and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of \(1~\text{A}\). What is the force per unit length on it when it is placed on a horizontal table and the direction of the current east to west?
1. \(3\times10^{-5}~\text{N m}^{-1}\)
2. \(2\times10^{-7}~\text{N m}^{-1}\)
3. zero
4. \(5\times10^{-7}~\text{N m}^{-1}\)

The horizontal component of the earth’s magnetic field at a certain place is 3.0 ×10^–5 T and the direction of the field is from the geographic south to the geographic north. A very long straight conductor is carrying a steady current of 1 A. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current is south to north?

$1. 3\times {10}^{-5} N m^{-1}$
$2. 2\times {10}^{-7} N m^{-1}$
$3. 0$
$4. 5\times {10}^{-7} N m^{-1}$

A \(100\) turn closely wound circular coil of radius \(10~\text{cm}\) carries a current of \(3.2~\text{A}\). The magnetic field at the centre of the coil is:
1. \(4\times10^{-3}~\text{T}\)
2. \(6\times10^{-3}~\text{T}\)
3. \(2\times10^{-3}~\text{T}\)
4. \(5\times10^{-3}~\text{T}\)$\mathrm{}$

A \(100\) turn closely wound circular coil of radius \(10~\text{cm}\) carries a current of \(3.2~\text{A}\). the magnetic moment of this coil is:
1. \(20~\text{A-m}^2\)
2. \(10~\text{A-m}^2\)
3. \(30~\text{A-m}^2\)
4. \(15~\text{A-m}^2\)$\mathrm{}$

A 100 turn closely wound circular coil of radius 10 cm carries a current of 3.2 A. The coil is placed in a vertical plane and is free to rotate about a horizontal axis that coincides with its diameter. A uniform magnetic field of 2T in the horizontal direction exists such that initially, the axis of the coil is in the direction of the field. The coil rotates through an angle of 90° under the influence of the magnetic field. What is the difference of magnitude of the torque on the coil in the initial and final position?
$1. 0$
$2. 10 N-m$
$3. 20 N-m$
$4. 15 N-m$

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-$m^2$.

$1.\mathrm{ 10} s^{-1}$
$2.\mathrm{ 30} s^{-1}$
$3.\mathrm{ 40} s^{-1}$
$4.\mathrm{ 20} s^{-1}$