Two concentric coplanar circular loops of radii r1 and r2 carry currents i1 and i2, respectively, in opposite directions (one clockwise and the other anticlockwise.) The magnetic induction at the centre of the loops is half of that due to i1 alone at the centre. If r2 = 2r1 , the value of i2/i1 is

Magnetic field at the centre due to smaller loopB1 =  μ04π .  2πi1r1                 ….(i)Due to bigger loop, B2 =  μ04π .  2πi2r2So, net magnetic field at centreB=B1−B2 =  μ04π × 2π  i1r1 − i2r2According to question, B=12  ×  B1⇒μ04π . 2π  i1r1 − i2r2 =12  ×  μ04π . 2πi1r1i1r1 − i2r2 = i12r1 ⇒ i2r2 ⇒ i12r1 ⇒i1i2 =1    r2 =2r1