The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is: [Take μ 0 = 4 π × 10 - 7 N A - 2 ]

Step-by-step solution

The perpendicular distance of centroid from any side, 1 2 3 m Magnetic field due to one side. B 1 = µ o I 4 π r [ c o s θ 1 + c o s θ 2 ] = μ 0 ( 10 ) 4 π r 1 2 3 c o s 30 ° + c o s 30 ° = 5 3 π μ 0 3 2 + 3 2 = 15 μ 0 π Net magnetic field B = 3 B 1 = 45 π μ 0 = 45 π × 4 π × 10 - 7 = 180 × 10 - 7 T = 18 μ T