Question

A long wire carries a current of 4.00 A. Find the energy stored in the magnetic field inside a volume of 1.00 mm3 at a distance of 10.0 cm from the wire.

Answer 1

Current flowing through the wire, i = 4.00 A

Volume of the region, V = 1 mm3

Distance of the region from the wire, d = 10 cm = 0.1 m

Magnetic field due to the current-carrying straight wire, B = μ0i2πr

The magnetic energy stored is given by

U=B2V2μ0=μ02i24π2r2×12μ0×VU=μ0i24π2r2×12×VU=(4π×10−7)×(4)2×(1×10−9)(4π2×10−2)×2U=2.55×10−14 J