A cell is connected between the points A and C of a circular conductor ABCD of centre `'O'.angle AOC = 60^(@)`. If` B_(​1) and B_(​2)` are the magnitudes of the magnetic fields at O due to the currents in ABC and ADC respectively, the ratio `(B_(1))/(B_(2))`, is

Options

A. 5
B. `1//5`
C. 6
D. 1

Answer

D

Explanation

Let lengths of ABC and ADC is `l_(1)` and `l_(2)` respectively. Then
`(_(1))/(l_(2)) = (360 - 60)/(60) = 5` Now `(i_(1))/(i_(2)) = (l_(1))/(l_(2)) = :. i_(2) = 5i_(1)`
Now `B_(1) = (5)/(6) ((mu_(o)i_(1))/(2r))` and `B_(2) = (1)/(6) ((mu_(o)i_(2))/(2r))`