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.

Area of the small flat search coil, A = 2 cm²= 2 x 10^-4 m²

Number of turns on the coil, N = 25

Total charge flowing in the coil, Q = 7.5 mC = 7.5 x 10^-3 C

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

Induced current in the coil, I = [Induced emf (e)]/R————————Eq-1

Induced emf is given as: e = —N dφ/dt……………………Eq-2

Where, dφ = Charge in flux

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

I = – (N dφ/dt)/R

=> I dt = -Ndφ/R —————————Eq-3

Initial flux through the coil,φi = BA

Where, B = Magnetic field strength

Final flux through the coil, φf = 0

Integrating equation (3) on both sides, we have

⌠Idt  = -N/R  _Φi⌠^Φf  d_{Φ                         { NOTE- “⌠” is sign of integration}}

But total charge ,Q = ⌠I dt.

Therefore, Q = -N/R (Φf-Φi) = -N/R (-Φi)= + NΦi/R

=> Q = NBA/R

Therefore,B = QR /NA

=    (7.5 x 10^-3 x 0.5)/(25 x 2 x 10^-4)

= 0.75 T

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