Question

A current of 2A flows through a circular coil of area 4π x 10-2 m2. The magnetic field at the centre

of the coil is

a) 6.28 x 10-6 T b) 628 x 10-6 T

c) 62.8 x 10-6 T d) 0. 628 x 10-6 T​

Answer 1

Given:

A current of 2A flows through a circular coil of area 4π x 10-2 m².

To find:

Magnetic field at the centre of the coil.

Calculation:

Let radius of coil be r ;

$\rm{ \therefore \: area = 4\pi \times {10}^{ - 2} }$

$\rm{ = > \: \pi {r}^{2} = 4\pi \times {10}^{ - 2} }$

$\rm{ = > \: {r}^{2} = 4 \times {10}^{ - 2} }$

$\rm{ = > \: r= \sqrt{4 \times {10}^{ - 2}} }$

$\rm{ = > \: r= 2 \times {10}^{ - 1} }$

$\rm{ = > \: r= 0.2 \: m}$

Now , magnetic field at centre of coil ;

$\therefore \: B = \dfrac{ \mu_{0}}{4\pi} \bigg \{ \dfrac{2\pi i}{r} \bigg \}$

$= > \: B = \dfrac{ \mu_{0}}{4\pi} \bigg \{ \dfrac{2\pi (2)}{(0.2)} \bigg \}$

$= > \: B = \dfrac{ \mu_{0}}{4\pi} \bigg \{ 20\pi \bigg \}$

$= > \: B = {10}^{ - 7} \times \bigg \{ 20\pi \bigg \}$

$= > \: B = 2\pi \times {10}^{ - 6}$

$= > \: B = 2 \times 3.14\times {10}^{ - 6}$

$= > \: B = 6.28\times {10}^{ - 6} \: tesla$

So , final answer is:

$\boxed{ \bf{\: B = 6.28\times {10}^{ - 6} \: tesla}}$