Download Document

Problem 3
An infinitely long wire has 5 amps flowing in it. A
rectangular loop of wire, oriented as shown in the
plane of the paper, has 4 amps in it. What is the force
exerted on the loop by the long wire?
Consider the coaxial cable shown below. This
represents an infinitely long cylindrical conductor
carrying a current i spread uniformly over its cross
section and a cylindrical conducting shell around it
with a current i flowing in the opposite direction. The
second i is uniformly spread over the cross section
of the shell. Find magnetic field everywhere.
b
a
c
i
Induced EMF and Inductance
1830s Michael Faraday
Joseph Henry
Faraday’s Law of Induction
The induced EMF in a closed loop equals the negative of the
time rate of change of magnetic flux through the loop
d B
EMF  
dt
 
d B
 E  dr   dt
There can be EMF produced in a
number of ways:
•
•
•
•
A time varying magnetic field
An area whose size is varying


A time varying angle between B and dS
Any combination of the above
S
S
 
d B  B  dS  B dS  BdS cos 
R
From Faraday’s law: a time
varying flux through a
circuit will induce an EMF
in the circuit. If the circuit
consists only of a loop of
wire with one resistor, with
resistance R, a current
EMF
i
R
Which way?
Lenz’s Law: if a current is induced by some
change, the direction of the current is such
that it opposes the change.
 
d B
 E  dr   dt
The Moving Circuit
There is a uniform magnetic field out of the
board. A rectangular circuit is pulled at a
constant speed to the right. What current
flows in the circuit if the total resistance of
the circuit is R?
S
The magnetic field between the poles of the
electromagnet is uniform, but its magnitude is
increasing at the rate of 0.020 T/s. The area
of the conducting loop in the field is 120 cm2,
and the total circuit resistance, including the
meter and the resistor, is 5.0 Ώ. Find the
induced EMF and the induced current in the
circuit.
 
 B  B  S  BS cos 0  BS
d B d ( BS ) dB


S  (0.020 T / s)(0.012 m 2 )  2.4 10  4 V  0.24mV
dt
dt
dt
Problem 3
• A rod with resistance R1 slides without
friction on two resistance-free tracks which
are connected by a resistor, R2. A wire,
carrying a current i, is parallel to the
tracks, in the same plane. Ignoring the
self-inductance of the circuit, calculate the
current that flows through R2 as a function
of the velocity of the rod.
Exercise 4
• An infinitely long wire has a current given
by i(t) = i0 sinwt where i0 and ω are
constants. A regular loop of wire is placed
near the wire. If the rectangular loop has
resistance R, what current will flow in it?
A Simple Generator
Induced EMF and Inductance
1830s Michael Faraday
Joseph Henry
B  i;   B;   Mi
M is mutual inductance