A long coaxial cable consists of two $$thin-walled$$ conducting cylinders with inner radius $$2$$ cm and outer radius $$8$$ cm. The inner cylinder carries a steady current $$0.1$$ A, and the outer cylinder provides the return path for that current. The current produces a magnetic field between the two cylinders. Find the energy stored in the magnetic field for length $$5$$ m of the cable. Express answer in $$nano-J$$ (use$$ $$ln2$$ $$=$$ $$0.7).

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Infinity Learn · Accepted Answer

The magnetic field inside is only due to the current of the inner cylinder.$$B=$$μ$$0i2$$$$π$$rMagnetic field energy density is not uniform in the space between the cylinders. At a distance r from the centre,μ$$B=B22$$μ$$0=$$μ$$0i28$$$$π$$$$2r2Energy$$ in volume of element $$(length$$ $$l)dUB=uBdV=$$μ$$0i28$$$$π$$$$2r22$$$$π$$$$ldr=$$μ$$0i2l4$$$$π$$drr $$UB=$$μ$$0i2l4$$π∫$$abdrr=$$μ$$0i2l4$$$$π$$lnbaUsing values, we get U $$=$$ $$7$$ nJ

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