Question

A long wire carrying current `i_(0)` is planced near a small cube of edge a at distance `d(d gt gta)` . Find the magnetic energy stored in the loop.

Answer 1

Magnetic field duw to a long wire
`B=(mu_(0)i_(0))/(2pid)`
Energy density
`u=(B^(2))/(2mu_(0))`
Magnetic energy stored in the cube
`U=uV`
`=B_(2)/(2mu_(0))a^(3)`
`=(1)/(2mu_(0))((mu_(0)i_(0))/(2pid))^(2)a^(3)`
`=(mu_(0)i_(0)^(2)a^(3))/(8pi^(2)d^(2))`