A circular loop of radius R carries a steady current. The magnetic field at the centre of the loop is B₀ . At a distance x from the centre on the axis of the loop, the magnetic field is found to be B₀ 27 . The value of x is:

Step-by-step solution

The magnetic field at the centre of a circular loop of radius R is given by: B_ center = ₀ I 2R = B₀ The magnetic field at a distance x on the axis of the loop is: B_ axis = ₀ I R² 2(R² + x²)^ 3/2 Given that B_ axis = B₀ 27 , we can write the ratio as: B_ axis B_ center = R³ (R² + x²)^ 3/2 = 1 27 Taking the cube root of both sides: R R² + x² = 1 3 Squaring both sides: R² R² + x² = 1 9 R² + x² = 9R² x² = 8R² x = 2 2 R Answer: 2 2 R