A battery is connected between two points `A and B` on the circumference of a uniform conducting ring of radius `r` and resistance `R` . One of the arcs `AB` of the ring subtends an angle `theta` at the centre . The value of the magnetic induction at the centre due to the current in the ring is

Options

A. propotation to `2 (180^(@)-theta)`
B. inversely proporational to r
C. zero, only if `theta=180^(@)`
D. zero, for all values of `theta`

Answer

D

Explanation

At A, the current is divided into two parts ADB and ACB. The resistance is proporational to length. The resistances `R_(1) and R_(2)` are in parallel.
`therefore(I_(1))/(I_(2))=(R_(2))/(R_(1))`

`therefore` The magnetic induction at O due to currents in the two parts will be equal but oppositely directed. Hence the resultant field is zero for any positions of the points A and B.