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.

Explanation

Here `r_1 = 5cm, r_2 = 10cm`
`=50,n_2 =100`
`Currents i_1 = i_2 = 5A`
(a) `B =(mu_on_1i_1)/(2r_1) +(mu_on_2i_2)/(2r_2)`
`=(4pixx10^(-7)xx50xx5)/(2xx5xx10^(-2) + (4pix10^(-7)xx100xx5)/(2xx10xx10^(-6)`
`=4pixx250xx10^(-6) + 4pixx250xx10^(-6)`
`=2xx4pixx250xx10^(-6) T`
`=2pixx10^(-3) T`
(b)Clearly, when currents are in opposite
direction.
B at centre = 0.