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 cm^(2)` 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 flowing in the coil (mesured by a ballistic galbanometer connected to the coil) is 7.5 mC. The resistance of the coil and galvanometer is `0.5 Omega`. Estimate the field strength of the magnet.

Explanation

Area of the small flat search coil, A = 2 `cm^(2) = 2 xx 10^(−4) m^(2)`
Number of turns on the coil, N = 25
Total charge flowing in the coil, Q = 7.5 mC = 7.5 `xx 10^(−3)` C
Total resistance of the coil and galvanometer, R = 0.50 `Omega`
Induced current in the coil,
`I=("Induced")/R`....(1)
Induced emf is given as:
`e=-N(dphi)/(dt)`...(2)
Where,
`dphi`= Charge in flux
Combining equations (1) and (2), we get
`I=-(N(dphi)/(dt))/(R)`
`Idt=-N/Rdphi`...(3)
Initial flux through the coil, `phi_(i)`=BA
Where,
B = Magnetic field strength
Final flux through the coil,`phi_(f)=0`
Integrating equation (3) on both sides, we have
`intIdt=(-N)/Runderset(phi_(i))overset(phi_(f))intdphi`
But total charge,`Q=intIdt`
`thereforeQ=(-N)/(R)(phi_(f)-phi_(i))=(-N)/R(-phi_(i))=+(Nphi_(i))/R`
`Q=(NBA)/R`
`thereforeB=(QR)/(NA)`
`(7.5xx10^(-3)xx0.5)/(25xx2xx10^(-4))=0.75T`
Hence, the field strength of the magnet is 0.75 T.