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Question
Derive an expression for energy stored in the magnetic field in terms of induced current.
Solution
- An induced emf is produced when the magnetic flux in a coil changes.
- The induced emf produced opposes the change and thus the energy expended to resist it in order to build up the magnetic field.
- This energy can be recovered as heat in the circuit's resistance.
- We know that, `e = -L(dI)/(dt)`
- The work done in moving a charge dq against this emf is
∴ dw = -e.dq = L`(dI)/(dt).dq = L.(dIdq)/dt`
∴ dw = L.I.dI ...........`(∴ (dq)/(dt) = I)`
Therefore, the total work is given by,
W = `∫ dw = ∫_0^1 L.I.dI`
∴ W = `1/2LI^2 = U_B` - This is the energy stored (UB) in the magnetic field.
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