A circular loop of radius r of conducting wire connected with a voltage source of zero internal resistance produces a magnetic field B at its centre. If instead, a circular loop of radius 2r, made of same material having the same cross section is connected to the same cross section is connected to the same voltage source, what will be the magnetic field at its centre?

Options

A. `(B)/(2)`
B. `(B)/(4)`
C. 2B
D. B

Explanation

The magnetic field at the centre of a circular conducting loop,
`B=(mu_(0)I)/(2r)`
[I= current in the loop and r= radius of the loop]
If the resistance of the loop in the first case is R, then the resistance in the second case,
R'=2R [ snice in the second case the length of the loop is doubled]
`:.` In the second case, current in the loop, `I'=(I)/(2)`
`:.B'=(mu_(0)I')/(2xx2r)=(mu_(0)xx(I)/(2))/(2rxx2)=(B)/(4)`