What is the radius of the solenoid?

An inductor in the form of a solenoid contains 410 turns and is 15.4 cm in length. A uniform rate of decrease of current through the inductor of 0.421 A/s induces an emf of 175 µV. What is the radius of the solenoid?
mm

asked Mar 6, 2012 in Physics

Being with the formula for inductance for a solenoid, which is

L = μN^2 * A/l  (*where L=inductance, μ0 = permeability of free space, N=number of turns, A=area, l=length)

Area = pi*r^2,

plugging this into the formula above we get:

L = μN^2 * (pi*r^2)/l

Now solve for r,

r = squareroot[(L*l)μN^2 * (pi)]

we are given the following values,

l = 15.4 cm = 15.4*10^-2 m

N = 410 turns

dI/dt = 0.421 A/s

Emf = 175 µV = 175*10^-6 V

Since we know the emf, we can calculate late L from the formula for emf:

Emf = -L*dI/dt

L = Emf / dI/dt

L = 175*10^-6 V / 0.421 A/s = 4.157*10^-4 H

Now we can plug this back into the formula for r and solve

answered Mar 12, 2012 by ~Expert~ (1,318 points)
selected Mar 14, 2012 by Joey33