A circular current carrying coil has a radius R . The distance from the centre of the coil, on the axis, where B will be 1 8 of its value at the centre of the coil is

Step-by-step solution

B= ₀ N i R^2 2 (R^2+x^2 )^ 3 / 2 aligned & = ₀ N i 2 R 1 [1+ x^2 R^2 ]^ 3 / 2 & =B_C 1 (1+ x^2 R^2 )^ 3 / 2 [ Let B_C= ₀ N i 2 R ] aligned B_C 8 = B_C (1+ x^2 R^2 )^ 3 / 2 [ B= B_C 8 ] array rlrl & (1+ x^2 R^2 )^ 3 / 2 & =8 & 1+ x^2 R^2 & =4 & x^2 R^2 & =3 & & x & =R 3 array