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 $2c{m}^2$ 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 ${90}^{\circ }$ 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 $\Omega$. Estimate the field strength of magnet.

Answer 1

$Q={\int }_{t_i}^{t_f}Idt$
$=\frac{1}{R}{\int }_{t_i}^{t_f}\epsilon dt$
$=-\frac{N}{R}{\int }_{{\Phi }_i}^{{\Phi }_f}d\Phi$
$=\frac{N}{R}({\Phi }_i-{\Phi }_f)$

$N=25,R=0.50\Omega ,Q=7.5\times {10}^{-3}C$

${\Phi }_f=0,A=2.0\times {10}^{-4}{m}^2$

$⟹{\Phi }_i=1.5\times {10}^{-4}Wb$

$B={\Phi }_i/A=0.75T$