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Inductance of Solenoid

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A solenoid of inductance L is connected, via a resistance R, to a battery of fixed
voltage V0. If the current is denoted by I(t), the voltage across the solenoid will be
VL(t) = LdI/dt . The switch is closed at t = 0.
(a) Determine I(t) and VL(t).
(b) What is the total energy delivered to the solenoid between t = 0 and t = 1?
(c) Assuming that L = μ0N2A/l, where N = number of turns, A = cross-sectional area,
and l = length, find the energy density of the magnetic field H stored within the

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Solution Preview

(a) The Ohm's law requires that

RI + LdI/dt = V_0 (1)

This is a linear differential equation. To solve it, we 1st solve its homogeneous version,

RI + LdI/dt = 0 (2)

by seeking the solution in the form

I = c?e^{at}. (3)

Substitution of this form into equation (2) yields the characteristic equation,

R + La = 0 (4)

from ...

Solution Summary

The inductance of solenoid is determined. The energy density of the magnetic field is found.