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

Answer

D

Explanation

For a current flowing into a circular arc, the magnetic induction at the centre is
Or `B=((mu_(0)i)/(4pir))theta`
In the given problem, the total current is divided into two arcs
`i theta=` constant

i.e. magnetic field at centre due to arc AB is equal and opposite to the magnetic field at centre due to arc ACB. Or the net magnetic field at centre is zero.