MHT CET202313 May 2023Morning ShiftPhysicsMagnetic Effects of CurrentActual
A circular coil of radius ' r ' and number of turns ' n ' carries a current ' I '. The magnetic fields at a small distance ' h ' along the axis of the coil (B_a ) and at the centre of the coil ( B _ c ) are measured. The ralation between B_c and B_a is
Options
- AB _ c = B _ a (1+ h ^2 r ^2 )
- BB _ c = B _ a (1+ h ^2 r ^2 )^ 1 2
- CB _ c = B _ a (1+ h ^2 r ^2 )^ 3 2
- DB _ c = B _ a (1+ h ^2 r ^2 )^ - 3 2
Correct answer
C. B _ c = B _ a (1+ h ^2 r ^2 )^ 3 2
Step-by-step solution
Magnetic field along the axis of the coil is: B _ a = ₀ 4 [ 2 nIr r ^2 ( r ^2+ h ^2 )^ 3 2 ] Magnetic field at the centre of the coil is: aligned B _ C & = ₀ 4 ( 2 nI r ) B _ C B _ a & = ( r ^2+ h ^2 )^ 3 2 r ^3 B _ C & = B _ a [1+ h ^2 r ^2 ]^ 3 2 aligned