Question

Calculate the magnetic field of a circular coil of 250 turns and of diameter 0.1m carrying a current of 7a at the centre of the coil

Answer 1

Given:

Circular coil has 250 turns , diameter of 0.1 m and current of 7 Amp.

To find:

Magnetic field at the centre of the coil.

Calculation:

For a circular coil , with n number of turns , the magnetic field is given as :

$\boxed{ \rm{B = n \times \dfrac{\mu_{0}}{4\pi} \times \bigg \{\dfrac{2\pi i}{r} \bigg \}}}$

Putting the available values :

$\rm{ = > B = 250 \times \dfrac{\mu_{0}}{4\pi} \times \bigg \{\dfrac{2\pi \times 7}{0.05} \bigg \}}$

$\rm{ = > B = 250 \times {10}^{ - 7} \times \bigg \{\dfrac{2\pi \times 7}{0.05} \bigg \}}$

$\rm{ = > B = 50 \times {10}^{ - 5} \times \bigg \{2\pi \times 7 \bigg \}}$

$\rm{ = > B = 7\pi \times {10}^{ - 3} \: tesla}$

So , final answer is :

$\boxed{ \large{ \red{ \sf{ B = 7\pi \times {10}^{ - 3} \: tesla}}}}$