Question

The earth's magnetic field at a given point is 0.5 × 10^-5 Wbm^-2. This field is to be annulled by magnetic induction at the centre of a circular conducting loop of radius 5.0 cm. The current required to be flown in the loop is nearly:
1. 0.2 A
2. 0.4 A
3. 4 A
4. 40 A

Answer 1

Correct Answer - Option 2 : 0.4 A

Given, Earth’s magnetic field at a point

B_E = 0.5 × 10-5 Wbm-2

The radius of a circular ring, r = 5 cm

So, for the field to be annulled by magnetic induction at the centre of the circular conducting loop of radius 5 cm, then B_E = B_R [Magnetic field at ring centre]

\(0.5 \times {10^{ - 5}} = \frac{{{\mu _0}i}}{{2r}}\)

\(0.5 \times {10^{ - 5}} = \frac{{{\mu _0}i \;\times\; 2\pi }}{{2r \;\times \;2\pi }}\)

\(\frac{{{\mu _0}}}{{\mu \pi }} = {10^{ - 7}}\)

\(0.5 \times {10^{ - 5}} = {10^7} \times \frac{{i\; \times\; 2\pi }}{{5\; \times\; {{10}^{ - 2}}}}\)

\(0.5 \times {10^{ - 5}} = \frac{{2\; \times \;3.14 \;\times\; {{10}^{ - 7}}}}{{5\; \times\; {{10}^{ - 2}}}} \times i\)

i = 0.4A