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

Given, area of coil, `A = 2 cm^(2) = 2 xx 10^(-4) m^(2)`
Number of turns of 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 the galvanometer,
`R = 0.5 Omega`
Initial magnetic flux linked with the coil when inside the magnetic field is
`phi_(1) = BA`
Final magnetic flux linked with the coil when outside the magnetic field
`phi_(2)=0`
Induced emf in the coil is
`epsilon=-N(dphi)/(dt)`
Induced current in the coil is
`I=(epsilon)/(R)=-(N)/(R)(dphi)/(dt)`
`:. Idt=-(N)/(R)dphi`
We know that,
`I=(dq)/(dt)impliesIdt=dq`
`implies dq=-(N)/(R)dphi`
Integrating, `int dq=-(N)/(R)int_(phi_(1))^(phi_(2))dphi`
`q=-(N)/(R)(phi_(2)-phi_(1))`
`q=-(N)/(R)(0-BA)=(NBA)/(R)`
`B=(qR)/(nA)`
`=(7.5 xx 10^(-3) xx 0.5)/(25 xx 2.0 xx 10^(-4))=0.75 T`