Class 12 NEET Physics Moving Charges and Magnetism

Question is not correct.
The magnetic field at the centre of the coil,
B=

µ0ni

2r

where r is the radius.

E

R

=i
∴ R∝2πr⇒R=cr, where c is a constant.
∴ In the first coil,
B1=

µ0ni1

2r1

=

µ0nE

2r1(cr1)

=

µ0nE

2cr12

If r1=2r2 B1=

µ0nE1

2c(2r2)2

=

µ0nE1

2c.4r22

B2=

µ0nE2

2cr22

As B1 will not be equal to B2 unless E1 is different from E2,E1 and E2 will not be the same.
It is wrong to ask what potential difference should be applied across them. It should be perhaps the ratio of potential differences.
In that case, B1=B2

E1

4

=E2⇒E1=4E2
∴

E1

E2

=4