A long straight solid metal wire of radius R carries a current I, uniformly distributed over its circular cross-section. Find the magnetic field at a distance r from axis of wire (i) inside and (ii) outside the wire.

Options

A. 0.02
B. `1:1`
C. `1:4`
D. `9//16`

Answer

D

Explanation

Magnetic field at a distance `x=(R)/(2)` from surface
inside `=(mu_(0)Ix)/(2piR^(2))=(mu_(0)I)/(4piR)`
Magnetic field at a distance `x=(R)/(2)` from surface
outside `=(mu_(0)I)/(2pi(x+R))=(mu_(0)I)/(3piR)`
Magnetic field energy density `=(B^(2))/(2mu_(0))`
`therefore` the ratio of energy density `=(B_(in)^(2))/(B_("out")^(2))=(9)/(16)`