A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is 10⁻¹⁴ J. The value of is _______. ( _o = 4 10⁻⁷ Tm/A, = 3.14 )

Step-by-step solution

The magnetic field at the centre of the circular loop is given by B = ₀ I 2R Substituting the given values, B = 4 10⁻⁷ 2 2 0.1 = 4 10⁻⁶ T The magnetic energy density is u = B^2 2 ₀ u = (4 10⁻⁶)^2 2 4 10⁻⁷ = 16 ^2 10⁻¹² 8 10⁻⁷ = 2 10⁻⁵ J/m ^3 The volume of the small cube is V = (1 mm )^3 = (10⁻³ m )^3 = 10⁻⁹ m ^3 The magnetic energy stored inside the cube is U = u V U = 2 10⁻⁵ 10⁻⁹ = 2 10⁻¹⁴ J Using = 3.14 , we get U = 2 3.14 10⁻¹⁴ = 6.28 10⁻¹⁴ J Comparing with 10⁻¹⁴ J, we get = 6.28 Answer: 6.28