AP EAMCET201922 Apr 2019Morning ShiftPhysicsMagnetic Effects of CurrentActual
The magnetic field normal to the plane of a coil of (N ) turns and radius (r ) which carries a current (i ) is measured on the axis of the coil at a distance (h ) from the centre of the coil. This is smaller than the field at the centre by the fraction,
Options
- A( 3 2 h^2 r^2 )
- B( 2 3 h^2 r^2 )
- C( 3 2 r^2 h^2 )
- D( 2 3 r^2 h^2 )
Correct answer
A. ( 3 2 h^2 r^2 )
Step-by-step solution
The magnetic field normal to the plane of a coil of (N ) turns and radius (r ) having current (i ) on the axis at a distance (h ) from the centre is given by ( aligned B_ axis & = ₀ N i r^2 2 (r^2+h^2 )^ 3 2 & = ₀ N i r^2 2 (r^2 )^ 3 / 2 (1+ h^2 r^2 )^ 3 2 = ₀ N i r^2 [1+ h^2 r^2 ]^ 3 2 2 r^3 aligned ) [From Binomial theorem, (( l +x)^n= 1 +n x )] (B_ axis = ₀ N i 2 r (1- 3 h^2 2 r^2 ) )...(i) Magnetic field on the centre of a circular current carrying coil is given by (B_ centre = ₀ N i 2 r )...(ii) From Eqs. (i)