Question

It is desired to measure the magnitude of field between the poles of a powerful loud speaker magnet. A small flat search coil of area 2 cm2 with 25 closely wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick 90° turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to coil) is 7.5 mC. The combined resistance of the coil and the galvanometer is 0.50 W. Estimate the field strength of magnet.

Answer 1

Let the magnetic field between poles of loud speaker magnet is B.

given, number of turns, N = 25

area of small flat search coil, A = 2cm² = 2 × 10^-4 m²

so, initial flux through the coil, $\phi=NBA$

= 25 × B × 2 × 10^-4 = 5 × 10^-3 B

final flux through the coil is zero.

let coil is taken out in time 't'.

so, magnitude of induced emf, E = $\frac{\Delta\phi}{\Delta t}$

= (5 × 10^-3 B)/t

current in the coil, I = E/R

= {(5 × 10^-3 B)/t}/0.5

= (10^-2 B)/t

total charge flowing in the coil, q = It

= 10^-2 B/t × t = 10^-2 B

given, total charge, q = 7.5mC = 7.5 × 10^-3 C

so, 7.5 × 10^-3 = 10^-2 B

or, B = 0.75T

hence, magnetic field between poles is 0.75T.