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 Ω. Estimate the field strength of magnet.

Answer 1

Area of the small flat search coil, A = 2 cm² = 2 × 10⁻⁴ m²

Number of turns on the coil, N = 25

Total charge flowing in the coil, Q = 7.5 mC = 7.5 × 10⁻³ C

Total resistance of the coil and galvanometer, R = 0.50 Ω

Induced current in the coil,

Induced emf is given as:

Where,

= Charge in flux

Combining equations (1) and (2), we get

Initial flux through the coil, = BA

Where,

B = Magnetic field strength

Final flux through the coil,

Integrating equation (3) on both sides, we have

But total charge,

Hence, the field strength of the magnet is 0.75 T.