Transcript Lecture #24 10/26/05

Faraday’s Law
10 
5T
10 m
As the bar moves a current is induced!
3 m/s
2m
dB
E 
dt
There are no batteries anywhere, so we say that a
current is induced, by an induced emf.
Hence, an electric current can be induced in a circuit by a changing
magnetic field, in the opposite direction to the change in flux.
Generality of Faraday’s Law
•Faraday’s law applies when moving a
wire in a magnetic field
dB
E 
dt
However, changing
magnetic fields also
produce an EMF.
What is the nature of the force?
It is not a magnetic force because the
charges are not necessarily moving
Changing magnetic fields must produce electric fields!
Faraday’s Law and Electric Fields
dB
E 
dt
q
E
 E  ds
dB
 E  ds   dt
Faraday’s Law and Electric Fields
dB
 E  ds   dt
. A cylindrical region of radius R = 3.0 cm contains a uniform magnetic field parallel to its
axis. The field is 0 outside the cylinder. If the field is changing at the rate 0.60 T/s,
the electric field induced at a point 2R from the cylinder axis is:
Using Faraday’s law: 2p (2R)E =-p(R2) dB/dt,
so E= (-(R2) /4) dB/dt=0.0045 V/m
Comparision of Induction
dE
 B  ds  0 I  0 0 dt
dB
 E  ds   dt
•No magnetic monopole, hence no magnetic current
•Electric fields and magnetic fields induce in opposite fashions
What is the combined resistance
of the mess at right?
A) 1.5 k
B) 12 k
C) 14 k
D) 21 k
9 k
3 k
3 k
6 k
3 k
2 k
R  R1  R2  3  3  6
1 1
1 1 1 1
 
  
R R1 R2 3 6 2
R  R1  R2  R3  3  9  2  14
3 k
A Multiloop Circuit
I1 + I3 = I2
1.5 – 3I2 = 0
9 – 5I1 – 3I2 = 0
I2 = 1.5/3 = 0.5 A
I1 = (9 – 3I2)/5 = 1.5 A
I3 = I2 – I1 = 0.5 – 1.5 = – 1 A
I1
–
+
9V
5
I2
3
1.5 V
– +
I3
What
Whatisisthe
thevoltage
conservation
loop rule
of
you
current
get applied
law associated
to the upper
with
loop?
the junction on the right?
A)
A) 9I1++5II21 =+ I3I
32=0
B)
B) 9I+1 +5II13 –=3I
I22 = 0
C)
C) 9I–2 +5II13+=3I
I12 = 0
D)
D) 9I1–+5II21 +
– 3I
I3 2==00
Odd Circuit
What is the current through the
resistor?
A) 3.6 A
B) 1.8A
C) 90 A
D) 0 A
–
+
9V
5
9V
– +
Four circuits have the form shown in the diagram. The capacitor is
initially uncharged and the switch S is open.
The values of the emf , resistance R, and the capacitance C for each of
the circuits are
circuit 1:
18 V, R = 3 , C = 1 µF
circuit 2:
circuit 3:
18 V, R = 6 , C = 9 µF
12 V, R = 1 , C = 7 µF
circuit 4:
10 V, R = 5 , C = 7 µF
Which circuit has the largest current right after the switch is closed?
Which circuit takes the longest time to charge the capacitor to
½ its final charge?
Which circuit takes the least amount of time to charge the capacitor to
½ its final charge?
Torque on a Loop
B=1T
2 cm
I = 1A
What is the torque on the wire?
A) 4p10-2Nm
D) p10-4Nm
B) p10-2Nm
C) 4p10-4Nm
Which direction does the torque twist the loop?
A) Right towards, left away
B) Right away, left towards
C) Top towards, bottom away
D) Bottom towards, top away
Quiz: Ampere’s Law
•Consider three wires with
current flowing in/out as shown
•Consider three different loops
surrounding the wires
X
Y
Which of the loops has the largest and
smallest integrals of the magnetic
field around the loops drawn?
A) X > Y > Z
C) Y > Z > X
B) X > Z > Y
D) Y > X > Z
2A
3A
1A
Z
Quiz
A)Remains the same
B) Reverses
C) Changes in magnitude but not direction
D)Changes to some other direction