Two circular coils 1 and 2 are made from the same wire but the radius of the 1st coil is twice that of the 2nd coil. What is the ratio of potential difference applied across them so that the magnetic field at their centres is the same ?

Magnetic field at the centre of a circular coil isB=μ04π × 2πirwhere i is current flowing in the coil and r is radius of coil.At the centre of coil 1,B1=μ04π × 2πi1r1                  …(i)At the centre of coil 2,B2=μ04π × 2πi2r2                  …(ii)But B1 = B2∴    μ04π  2πi1r1=  μ04π  2πi2r2  or  i1r1  =i2r2As r1 = 2r2∴    i12r2  =i2r2  Or  i1  =  2i2        …(iii)Now, ratio of potential differencesV2V1= i2 ×  r2i1 ×  r1  =i2 ×  r22i2 ×  2r2 =14∴    V1V2= 41