Question

a long coaxial cable consits of two thin-walled conducting cyclider carries a steady current `0.1 A`, and the outer cylinder provides the return path for that current. The current produced a magnetic field between the two cylinders. Find the energy stored in the magnetic field for length `5m` of the cable. Express answer in Nj (use `1n2 = 0.7`).

Answer 1

Correct Answer - 7


The magnetic field inside is only due to the current of the inner cylinder.
`B = (mu_(0)i)/(2pir)`
Magnetic field energy density is not uniform in the space between the cylinders. At a distance `r` from the centre,
`u_(B) = (B^(2))/(2mu_(0)) = (mu_(0)i^(2))/(8pi^(2)r^(2))`
Energy in volume of element (length l)
`dU_(B) = u_(B)dV = (mu_(0)i^(2))/(8pi^(2)r^(2))(2pirl)dr = (mu_(0)i^(2)l)/(4pi)(dr)/(r )`
`U_(B) = (mu_(0)i^(2)l)/(4pi) int_(a)^(b)(dr)/(r ) = (mu_(0)i^(2)l)/(4pi)ln(b)/(a)`
Using values, we get `U = 7 nJ`