Two circular coils, each of 100 turns, are held that one lies in the vertical plane and the other in the horizontal plane with their centres coinciding. The radii of the vertical and the horizontal coils are respectively 20 cm and 30 cm. If the directions of the currents in them are such that the earth's magnetic field at the centre of the coils is exactly neutralised, then calculate the current in each coil. (Horizontal component of earth's magnetic field`=27.8 Am^(-1)`, angle of dip`=30^(@)`

Answer

A, B, D

Explanation

As the field due to a current-carrying coil is along its axis.the vertical coil will produce horizontal field not horizontal coil vertical, i.e.,
`mu_(0)/(4pi)(2piN_(V)l_(V))/(R_(V))=B_(H)` and `mu_(0)/(4pi)(2piN_(H)l_(H))/(R_(H))=B_(V)`
But as `tanphi=(B_(V))/(B_(H)),B_(V)=B_(H) tan phi=(B_(H))/sqrt3 [as phi=(phi//6)]`
and `1A/m=4pixx10^(-7)(Wb)/m^(2)`
so `10^(-7)(2pixx100xxI_(v))/0.2=4pixx10^(-7)xx27.8`
i.e.,`I_(v)=1112xx10^(-4) A`
and `10^(-7)(2pixx100xxI_(H))/0.3=4pixx10^(-7)xx27.8/sqrt3`
i.e.,`I_(H)=556sqrt6xx10^(-4) A`