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A solenoid of length l = 50 cm, cross-se...

A solenoid of length l = 50 cm, cross-sectional area `A= pi (0.5)^2 m^2` has an axial magnetic field of B = 0.1 T. Find the value of
magnetic energy

Text Solution

Verified by Experts

Magnetic field at any point inside the solenoid is
`B = (mu_0NI)/l`
`implies l= ((Bl)/(mu_0N))" "...(i)`
If Lis self-inductance of solenoid, then
`L = ((mu_0N^2A)/(l)) " "....(ii)`
(a) Magnetic energy store `=1/(2)Li^2`
From Eqs. (i) and (i), we have
`=1/2((mu_0N^2A)/(l)) ((Bl)/(mu_0N))^2`
`=1/2 xx((0.1)^2 xx(0.5)xxpixx(0.5)^2)/(4pi xx10^(-7))`
`= 1.56xx10^3J`
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