Two concentric coplanar circular loops made of wire, with resistance per unit length `lambda` , have radii `r_(I)` and `r_(2)(r_(2) gt gtr_(I))` . A potential difference `(alpha+betat)` is applied to the larger loop, where `t` is time. Calculate current in the smaller loop.

Explanation

Current in the larger loop `i=(alpha+betat)/(r_(2))` `R_(2)` : resistance of larger loop
Magnetic field due to larger loop at centre `B_(2)=(mu_(0)i)/(2r_(2)`n (assumed uniform in loop(1))
Flux through smaller loop
`phi_(1)=B_(2)A_(1)=(mu_(0)i)/(2r_(2)).pir_(1)^(2)=(mu_(0)(alpha+betat).pir_(1)^(2))/(2r_(2)R_(2)`
Induced emf in loop (1)
`e_(1)=(dphi_(1))/(dt)=mu_(0)(betapir_(1)^(2))/(2r_(2)R(2)`
Current in smaller loop
`i_(1)=(e_(1))/(R_(1))=(mui_(0)betapir_(1)^(2))/(2r_(2)R_(1)R_(2))`
`R_(1)=lambda.2pir_(1)` , `R_(2)lambda.2pir_(2)`
`i_(1)=((mu_(0)betapir_(1)^(2))/(2r_(2).2lambdapir_(1).2lambdapir_(2)))`
`=(mu_(0)brtar_(1)^(2))/(8lambda^(2)pir_(r)^(r))`