Download Physics Lecture #30

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Wed. Feb. 18 – Physics Lecture #30
Magnetic Fields
1. Magnetic Fields
2. Magnetic Moments & Torque
3. Ampere’s Law
1
2
Warm-Up, Discuss with Neighbors: Wire 1 carries current I going up as
shown. Wire 2 is a distance d away from wire 1, and carries current I going
down as shown.
Do the wires attract, repel, or something else?
1. Up
2. Down
a) What is the direction of the magnetic field at the
location of wire 2 due to the current in wire 1?
b) What is the direction of the magnetic force
acting on wire 2 due to the magnetic field from
wire 1?
3. Right
4. Left
5. Into page
6. Out of page
0. No direction/zero
Magnetic Field of Special Current Configurations
Axis of Loop of radius R, distance x
from center:
 0 2 I  R 2
B
4 ( x 2  R 2 )3 /2
Direction: fingers along current;
thumb along magnetic moment
Center of Loop of radius R, so that x = 0:
B
 0 2 I  0 I

4 R
2R
Direction: fingers along current;
thumb in field direction
Center of Arc of radius R, angle Dq:
 0 IDq  0 I Dq
B

4 R
2 R 2
Direction: fingers along current;
thumb in field direction
Axis of bar magnet with moment ,
distance x from center:
 0 2
B
4 x 3
Direction: magnetic moment
from South pole to North pole
Axis of long solenoid, away from edges,
with n turns per meter:
B   0 nI
Direction: fingers along current;
thumb in field direction
Long (“infinite”) Straight Wire, distance r
away from wire:
B
0 2I
4 r
Direction: thumb along current;
fingers curl in field direction
Two long straight wires are the same distance 0.5 m from
the origin. The wire on the y-axis has current 0.75 A going
into the page. The wire on the x-axis has current 1 A
coming out of the page.
What is the magnetic field (magnitude and direction)
at the origin?
A single piece of wire is bent so that it includes
a circular loop of radius a, as shown. A current I
flows in the direction indicated. Determine the
magnetic field (magnitude and direction) at the
center of the loop.
I
a
I
I
ConceptCheck: A square loop of wire with sides of
length L carries a current I in a clock-wise direction; the
current loop is in a uniform magnetic field B that is in
the plane of the page and pointing to the right, as
shown.
a) What is the direction of the magnetic
force acting on the right-most piece of loop?
1. Up
b) What is the direction of the net magnetic force
acting on the entire loop?
2. Down
3. Right
c) What is the direction of the net torque acting on the
entire loop? (Take center of loop as reference point.)
4. Left
5. Into page
Assuming the loop started from rest, what would be its
subsequent motion?
6. Out of page
0. No direction/zero
A current loop (N = 10, A = 0.01 m2 , I = 1 A,) makes an
angle of 30o with a uniform magnetic field of magnitude
0.2 T directed to the right, as shown in the figure. Assume
the current is going into the page at the lower left hand
part of the loop and out of the page at the upper right
hand part of the loop, as indicated on the sketch.
30o
What is the equivalent magnetic moment (magnitude and direction) of this
current loop?
What is the torque (magnitude and direction) acting on the current loop?
Gauss’s Law for Electricity?
Gauss’s Law for Magnetism?
Ampere’s Law?
A long conducting rod of radius R carries a non-uniform current density given by
J = J0r/R, where J0 is a constant and r is the radial distance from the axis of the
rod.
a) Use Ampere’s Law to determine the magnetic field strength outside the rod in
terms of the enclosed current.
b) Use integration to determine the enclosed current.
c) Use Ampere’s Law to determine the magnetic field strength inside the rod.