Question

A long coaxial cable consists of two hollow concentric cylinders of radii a and b. The central conductor of the cable carries a steady current I and outer conductor provides the return path of the same current. Calculate the energy stored in the magnetic field 'l' of such a cable –

• A. $\frac { \mu _ { 0 } I ^ { 2 } \ell } { 4 \pi }$log_e
• B. $\frac { \mu _ { 0 } I ^ { 2 } \ell } { 4 \pi }$log_e
• C.
• D. $\frac { \mu _ { 0 } I ^ { 2 } \ell } { 4 \pi }$log_e

Answer 1

Answer: (A)

$\frac { \mu _ { 0 } I ^ { 2 } \ell } { 4 \pi }$log_e

Answer 2

B = $\frac { \mu _ { 0 } \mathrm { I } } { 2 \pi \mathrm { r } }$

Volume of element = 2prdr × l Energy density

= = $\frac { \mu _ { 0 } ^ { 2 } I ^ { 2 } } { 4 \pi ^ { 2 } r ^ { 2 } }$

Energy = × 2prdrl