The magnetic field due to current carrying circular loop of radius 6 ~cm at a point on the axis at a distance of 8 ~cm from centre is 27 T . The magnetic field at the centre of the current carrying loop is.

Step-by-step solution

( Magnetic field due to a current carrying coil of radius R on its axis at a distance x from its centre is B_ axis = ₀ N I R^2 2 (x^2+R^2 )^ 3 2 Here, x=8 ~cm ,=8 10⁻² ~m R=6 ~cm =6 10⁻² ~m and B=27 T =27 10⁻⁶ ~T Substituting these values in eq. (i), we get aligned 27 10⁻⁶ & = ₀ N I (6 10⁻² )^2 2 [ (8 10⁻² )^2+ (6 10⁻² )^2 ]^ 3 / 2 & = ₀ N I (6 10⁻² )^2 .264 10⁻⁴+36 10⁻⁴ ]^ 3 / 2 27 10⁻⁶ & = N I 36 10⁻⁴ 2 (10⁻² )^ 3 / 2 27 10⁻⁶ & = ₀ N I 36 10⁻⁴ 2 10⁻³ ₀ N I & = 27 10⁻⁶ 2 10⁻³ 36 10⁻⁴ & = 3 2 10⁻⁵ units aligned Now