The correct option is C R2
Let i be the current flowing in the loop B.
Magnetic field at loop A due to loop B is given by
BA=μ0iR22(R2+x2)3/2
So, magnetic flux passing through loop A is
ϕA=BA(πr2)
ϕA=μ0iR22(R2+x2)3/2(πr2)
ϕA=μ0πir2R22(R2+x2)3/2
Applying Faraday's law of induction,
EA=−dϕAdt
EA=−μ0πir2R22(−32)(R2+x2)−5/2(2x)
EA=3μ0πir2R22x(R2+x2)5/2
As we know that EA will be maximum when, dEAdx=0
∴dEAdx=ddxx(R2+x2)5/2=0
[1×(R2+x2)5/2]−[5x2(R2+x2)3/2(2x)]=0
R2+x2−5x2=0
x=±R2
Hence, option (C) is correct.