(i) Two circular coils of raddii `5.0 cm` and `10 cm` carry equla currents of `1 A`.The coils have `50` and `100` turns respectively and are placed in such a way that their planes as well as the centre coincide.Find the magnitude of the magnetic field `B` at the common centre when the currents in the coils are (a) in the same sense ,(b) in the opposite sense.
(ii) If the outer coil of the above problem is rotated through `90^(@)` about a diameter,what would be the magnitude of the magnetic field `B` at the centre?

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`