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=2r2B1=
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