Answer to Question #141745 in Electricity and Magnetism for Sridhar

Question

A circular coil consists 70 closely wound turns and has a radius of 10cm. An externally produced magnetic field of magnitude 2×10^(-3)T is applied perpendicular to the coil.The net flux through the coil is found to vanish when the current in the coil is 2.2A. The inductance of the coil is
Ans 3mH

Answer 1

Φ = BA

The flux over the coil, equals the flux over one turn multiplied by the number of turns:

Φ_c = NΦ

Φ_c = NBA

The area of the coil is given by A = πR², hence

Φ_c = πNBR²

$Φc = π(70.0)(2.0 \times 10^{-3}\;T)(10 \times 10^{-2} \;m)^2 = 4.4 \times 10^{-3} \;Wb$

The net magnetic flux through the coil is zero, so the magnetic flux produced by the coil is given by equation:

$L = \frac{Φ_c}{I}$

$L = \frac{4.4 \times 10^{-3} \;Wb}{2.2 \;A} = 2 \times 10^{-3} \;H$

Answer: 2 mH