Question

A circular coil has a 10.0 cm radius and consists of 30 closely wound turns of wire. An externally produced magnetic field of 2.6 mT is perpendicular to the plane of the coil.

(a) if there is no current in the loop, what is the magnetic flux through the coil?
(b) When the current in the coil is 3.8 A in certain direction, the net flux through the coil is found to vanish. What is the inductance of the coil

Answer 1

(a) 0.00245 Wb

(b) 0.000645 H

Step-by-step explanation:

(a) The magnetic flux, Ф, through a coil of radius, r, having N turns due to a magnetic field, B, is given as:

Ф =
`NBA`

where A = area of coil =
`\pi r^2`

Ф = NB
`\pi r^2`

Ф =
`30 * 2.6 * 10^(-3) * \pi * 0.1^2`

Ф = 0.00245 Wb or
`2.45 * 10^(-3) Wb`

(b) If the magnetic flux through the coil vanishes, the magnetic flux due to the coil will be:

Ф =
`LI`

where L = inductance in the coil and I = current in the coil

Therefore:

L = Ф/I

L = 0.00245/3.8

L = 0.000645 H or
`6.45 * 10^(-4) H`