COMEDK2012PhysicsMagnetic Effects of Current
The ratio of the magnetic fields at the centre of a circular coil carrying current to that at a point whose distance is half of the radius of the coil is
Options
- A2 5 : 8
- B5 5 : 8
- C5 5 : 4
- D2 5 : 4
Correct answer
B. 5 5 : 8
Step-by-step solution
The magnetic field due to a circular coil carrying current at its axis is B_ x = ₀ 4 2 N i r² (x²+r² )^ 3 / 2 ...(i) At centre of coil, B_ c = ₀ 4 2 N i r ...(ii) From Eqs. (i) and (ii), we get B_ c D_ x = (x²+r² )^ 3 / 2 r r² At, x= r 2 , B_ c B_ x = ( r² 4 +r² )^ 3 / 2 r³ = ( 5 4 )^ 3 / 2 r³ r³ = 5 5 8 or 5 5 : 8