Two circular coils `C_1` and `C_2` each of 100 turns are held in such a way that `C_1` lies in vertical plane and the other `C_2` in the horizontal plane, with their centres coinciding. The radii of the coils are `r_1=20cm` and `r_2=30cm`. The directions of currents `I_1` and `I_2` passed through the two coils are such that earth's magnetic field at the common centre is neutralised completely. If `H=27*8Am^-1` and angle of dip is `30^@`. Calculate the values of `I_1` and `I_2`.

Explanation

Current through coil `C_1` in vertical plane produces a field that would neutralize H.
`:. B_1=(mu_0n_1I_1)/(2r_1)=mu_0H` `:. I_1=(2r_1H)/(n_1)=(2xx20xx10^-2xx27*8)/(100)=0*11A`
Similarly current through coil `C_2` in horizontal plane produces a field that would neutralize V
`:. B_2=(mu_0n_2I_2)/(2r_2)=mu_0V` or `I_2=(2r_2V)/(n_2)=(2r_2(H tan delta))/(n_2)=(2xx30xx10^-2xx27*8tan30^@)/(100)=0*096A`