Two circular coil of radii 5cm and 10cm carry equal currents of 2A. The coils have 50 and 100 turns, respectively, and are placed in such a way that their planes as well as their centers coincide. Magnitude of magnetic field at the common centre of coils is

Options

A. `8pixx10^-4T` if currents in the coils are in same sense
B. `4pixx10^-4T` if current in the coils are in opposite sense
C. zero if currents in the coils are in opposite sense
D. `8pixx10^-4` T if currents in the coils are in opposite sense

Answer

A, C

Explanation

`B_1=(mu_0N_1iI_1)/(2R_1)`
`=((4pixx10^I-7)(50)(2))/(2(5xx10^-2))`
`=4pixx10^-4T`
`B_2=(mu_0N_2i_2)/(2R_2)`
`=((4pixx10^-7)(100)(2))/((2)(10xx10^-2))`
`=4pixx10^-4T`
When currets are in the same direction then
`B_("net")=B_1+B_2`
When curents are in the opposite direction, then
`B_("net")=B_1-B_2`