Question

Learning Goal: To practice Problem-Solving Strategy 30.1 Electromagnetic Induction. A coil of wire contains N turns and has an electrical resistance R. The radius of each turn is a. Initially, inside the coil there exists a uniform magnetic field of magnitude B0 parallel to the axis of the coil. The magnetic field is then reduced slowly. The current induced in the coil is I. How long does it take for the magnitude of the uniform field to drop to zero?

Answer 1

Answer:

Time interval for which magnetic field reduced to ZERO is given as

$t = \frac{NB_0\pi a^2}{RI}$

Explanation:

As we know that the flux linked with one coil is given as

$\phi = B_0 A$

$\phi = B_0(\pi a^2)$

now total flux of all coils is given as

$\phi = NB_0\pi a^2$

now let say the flux is reduced to ZERO after time "t"

so as per Faraday's law EMF induced in the coil is given as

$EMF = \frac{NB_0\pi a^2 - 0}{t}$

now the current in the coil is given as

$I = \frac{EMF}{R}$

$I = \frac{NB_0\pi a^2}{Rt}$

so the time interval is given as

$t = \frac{NB_0\pi a^2}{RI}$