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

Here, `A = 2 cm^(2) = 2 xx 10^(-4) m^(2) , N = 25`
Final flux, `phi_(f) = 0`
`Q = 7.50 mC = 7.5 xx 10^(-3) C, R = 0.5 Omega, B = ?`
We know, `I = (e)/(R ) = (-N d phi//dt)/(R )`
`I dt = (-N)/(R ) d phi`
As change, `Q = int I dt = int_(phi_(i))^(f^(phi)) - (N)/(R ) d phi = (-N)/(R ) (phi_(f) - phi_(i)) = (N)/(R ) (phi_(i) - phi_(f)) = (N)/(R ) phi_(i)`
Now, initial flux/turn when coil is normal to the field, `phi_(i) = BA`
`:. Q = (NBA)/(R )` or `B = (QR)/(NA) = (7.5 xx 10^(-3) xx 0.5)/(25 xx 2 xx 10^(-4)) = 0.75` tesla