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PROBLEM SET 2
ECE 312 Autumn Quarter 2010
Assigned:
October 1st
Due:
October 8th in class
Instructor: Joel Johnson
Problem 1
A single loop of wire of radius
b
is centered on the
z
axis in a cylindrical coordinate system.
Assume that a voltage source
Vt
()
is connected to this loop through a resistance
R
; when
is
constant in time, a current
φ
ˆ
It
flows in the loop. This current produces a magnetic flux density
Bz
ˆ
μ
0
2
b

=
inside the area bounded by the loop, where
t
indicates time in seconds. (Note this is
only an approximation of the true magnetic flux density that would result from use of the Biot
Savart law.) Now assume that
is no longer constant in time.
z
b
φ
ˆ
R
+

V
1
2
(a) Find the magnetic flux linking the loop.
(b) Calculate the EMF induced in the loop by Faraday’s law.
(c) Comparing your part (b) answer with circuit theory concepts, what is the approximate
inductance of this wire? Discuss any sign changes you need to make. Note this is
approximate because our original magnetic flux density was approximate.
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This note was uploaded on 01/11/2012 for the course ECE 312 taught by Professor Johnson,j during the Fall '08 term at Ohio State.
 Fall '08
 Johnson,J
 Electromagnet, Volt

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