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 voltage source, what will be the magnetic field at its centre?

Options

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

Answer

B

Explanation

Field due to circular loop of radius r of conducting wire at the centre is
`B= (mu_(0))/(2) (I)/(r )` …(i)
For same material and having the same cross section. When radius of loop is doubled, the resistance of the circuit is also doubled. Therefore the current in the circuit becomes half.
ie., `I. =(I)/(2) and r.= 2r`.
`:.` Field due to new circular loop is `B.= (mu_(0))/(2) (I.)/(r.) or B. = (mu_(0)I)/(8r)= (1)/(4)B` [using (i)]