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Q.

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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answer is 7.

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Detailed Solution

The magnetic field inside is only due to the current of the inner cylinder.B=μ0i2πrMagnetic field energy density is not uniform in the space between the cylinders. At a distance r from the centre,μB=B22μ0=μ0i28π2r2Energy in volume of element (length l)dUB=uBdV=μ0i28π2r22πldr=μ0i2l4πdrr UB=μ0i2l4π∫abdrr=μ0i2l4πlnbaUsing values, we get U = 7 nJ
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