Unformatted text preview: taking integrals of derivative equations, here is another path.
Since the induced current is constant, and the area of the loop is not changing in time (nor is the
area vector changing with respect to the B ﬁeld), the only option to create a changing ﬂux is
if the B ﬁeld is changing in time. The time dependence of the B ﬁeld must be such as to produce
a constant after taking a time derivative. So in this case, you know that B must increase linearly
with time, or B(t) ~ Ct+D, where C and D are constants.
The problem says that at t=0, B=0, so this condition tells you that D=0. You can get the constant C
by recognizing that EMF=IR=C*a*b, so C=IR/ab. Thus you can determine that the required B
ﬁeld as function of time is B=IRt/ab Printed by Mathematica for Students Physics 7D Quiz A
Week 10 Name:_______________________
ID #: _______________________ 1) A wire loop of radius a and resistance R is exposed to a changing magnetic field such that a constant current I is
in it. a) Initially the magnetic field is zero, what is the direction of a magnetic field B that would make the
induced current travel clockwise? (Into Page or Out of Page) b) Find the magnitude of the of the magnetic field B as a function of time needed to maintain a constant
current in the loop. Express B in terms of t, I, R and a. Ignore the
field produced by the current loop itself. Printed by Mathematica for Students 2 QuizA_week10.nb Solutions
Using lenz’s law the field must me increasing in the direction out of the page since the loop will need to produce
a field to oppose the change in flux.
1b) Since all we care about is the magnitude I will drop the signs in Faraday’s law
‚t Ÿ ‚
‚t = B=Ÿ B‚A
p a2 IR
p a2 ‚t = I Rt
p a2 Printed by Mathematica for Students 2 Discussion_week10.nb Printed by Mathematica for Students...
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This note was uploaded on 09/23/2013 for the course PHYSICS 7D 7D taught by Professor Barwick during the Spring '11 term at UC Irvine.
- Spring '11