The ratio of magnetic field at the centre of the current carrying circular loop and its magnetic moment is ' x '. When both the current and radius are tripled, then the ratio will be

Step-by-step solution

Magnetic field at the centre of a circular loop is B = ₀ I 2R Magnetic moment of the loop is M = I R^2 The ratio is x = B M = ₀ I 2R I R^2 = ₀ 2 R^3 When current and radius are tripled, I' = 3I and R' = 3R New magnetic field B' = ₀ (3I) 2(3R) = ₀ I 2R = B New magnetic moment M' = (3I) (3R)^2 = 27 I R^2 = 27 M New ratio x' = B' M' = B 27M = x 27 Answer: x 27