The earth's magnetic field at a certain point is \( 7.0 \times \) \( 10^{-5} T \). This field is to be balanced by a magnetic field at the centre of a circular current carrying coil of radius \( 5 cm \) by suitably orienting it. If the coil has 100 turns then the required current (up to nearest integer) is \( X \) \( mA \). Find \( X \).

Question

The earth's magnetic field at a certain point is \( 7.0 \times \) \( 10^{-5} T \). This field is to be balanced by a magnetic field at the centre of a circular current carrying coil of radius \( 5 cm \) by suitably orienting it. If the coil has 100 turns then the required current (up to nearest integer) is \( X \) \( mA \). Find \( X \).

Answer 1

Magnetic induction due to circular coil at centre

\(B =\frac{\mu_0NI}{2R}\)

Then 

\(I = \frac{B.2R}{\mu_0N}\)

\(I = \frac{7\times 10^{-5}\times 2\times 0.05}{4\pi \times 10^{-7}\times 100}\)

\(I = \frac{7\times 10^{-5}\times 2\times 0.05}{4\times 3.14 \times 10^{-7} \times 100}\)

\(I = \frac{0.7\times 10^{-5}}{12.56\times 10^{-5}}\)

\(I = 0.055\)

\(I = 55\times 10^{-3} A\)

\(I = 55 mA\) 

Then 

\(X = 55\)