Two coaxial long solenoids of equal lengths have currents i 1 and i 2 , the number of turns per unit length n 1 and n 2 and radii r 1 and r 2 r 2 r 1 respectively. If n 1 i 1 = n 2 i 2 and the two s

Question

Two coaxial long solenoids of equal lengths have currents i 1 and i 2 , the number of turns per unit length n 1 and n 2 and radii r 1 and r 2 r 2 > r 1 respectively. If n 1 i 1 = n 2 i 2 and the two solenoids carry currents in the opposite sense, the magnetic energy stored per unit length is

TestHub · Accepted Answer

The magnetic field is non-zero only in the region between the two solenoids, where $B = µ_{0} n_{2} i_{2}$

$∴$ Energy stored per unit volume

$= \frac{B^{2}}{2 μ_{0}} = \frac{μ_{0} n_{2}^{2} i_{2}^{2}}{2}$

The energy per unit length = energy per unit volume $\times$ area of cross section where $B \neq 0$

= $\frac{μ_{0} n_{2}^{2} i_{2}^{2}}{2} π [r_{2}^{2} - r_{1}^{2}]$

$= \frac{μ_{0} n_{1}^{2} i_{1}^{2}}{2} [π r_{2}^{2} - r_{1}^{2}]$ , since $n_{1} i_{1} = n_{2} i_{2}$

Physics - Magnetism Question with Solution | TestHub

Options:

Doubts & Discussion