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?

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

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 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. \(794~\text{A}\)