A metallic coil of N turns of radius r, resistance R, and inductance L is held fixed with its axis along a spatial uniform magnetic field `bar(B)` whose magnitude is given by `B_(0) sin(omegat)`.
Write the equation for the current i in the coil.
given that `B_(0)=1.00"tesla", N=10, r=10cm, omega=1000.0 rad s^(-1), R=10.0Omega, L-100,0mH`.

Answer

A

Explanation

(a)`iR+L(di)/(dt)=-Npia^(2)B_(0)omega cos omegat`
(b)`i=(Npi a^(2) B_(0)omega (R cos omegat +omegaL sin omegat))/(R^(2)+omega^(2)L^(2))`
(c )`(dF)/(dl)=-(NB_(0)^(2))/(2(R^(2)+omega^(2)L^(2)))(Rsin omegat cos omegat+omega L sin^(2)omegat)`
`(dF)/(dl)|_(av) =-(NB_(0)^(2) pia^(2)omega^(2)L)/(2(R^(2)+omega^(2)L^(2)))=(dF)/(dl)|_(osc)=-(NB_(0)^(2) pia^(2)omega)/(2(R^(2)+omega^(2)L^(2)))(Rsin 2omegat cos omegat-omega L cos^(2)omegat)`
(d)`(dF)/(dl)|_(av) =1.55 N m^(-1)`
(e)`i`.The frequency of the sounds is `120 Hz`.