Two circular coils of radii 5.0 cm and 10 cm carry equal currents of 2.0 A. The coils have 50 and 100 turns respectively and are placed in such a way that their planes as well as the centres coincide. Find the magnitude of the magnetic field B at the common centre of the coils if the currents in the coils are (a) in the same sense (b) in the opposite sense.

Answer

A, B, D

Explanation

(i)`(a)B_(Net)=(mu_(0)N_(1)l)/(2r_(1))+(mu_(0)N_(2)l)/(2r_(2))=(mu_(0)I)/2[N_(1)/r_(1)+N_(2)/r_(2)]=(4pixx10^(-7)xx1)/2[20/10^(-2)]=8pixx10^(-4)wb//m^(2)`
(ii)`B_(Net)=(mu_(0)N_(1)l)/(2r_(1))=0`
(iii)`B_(Net)=sqrt(B_(1)^(2)+B_(2)^(2))=sqrt2B_(1)=sqrt2(mu_(0)N_(1)I)/(2r_(1))=4sqrt2pixx10^(-4)T`