Two circular coils made of similar wires but of radii 20 and 40cm are connected in parallel. Find the ratio of the magnetic fields at their centers.

Answer

`4`

Explanation

(4) When the coils are connected in parallele, the ratio of currents
flowing in these coils will be equal to reciprocal of the ratio of
their resistances,
`:. (i_1)/(i_2)=(R_2)/(R_1)=(rho(l_2//A))/(rho(l_1//A))`
(as both the coils are made of similar wires)
`implies (l_2)/(l_1)=(2pir_2)/(2pir_1)=(r_2)/(r_1) :. (B_1)/(B_2)=((mu_0i_1)//2r_1)/((mu_0i_2)//2r_2)`
`:. (B_1)/(B_2)=(i_1)/(i_2)xx(r_2)/(r_1)[:' (i_1)/(i_2)=(r_2)/(r_1)]`
`:. (B_1)/(B_2)=(r_2^2)/(r_1^2)=(40/20)^2=4/1=4`