Phy 132 - Assignment 8:
A. 1. a. Yes. Any charged object produces an electric field.
b. No. Only moving charges produce a magnetic field.
2.
B. 1. a. Yes. Any charged object produces an electric field.
b. Yes. The electrons are moving, so they qualify as a current.
2.
C.
D. 1. a. No. The wire has no net charge. It contains equal numbers of electrons
(which happen to be moving) and positive copper ions (with fixed positions).
b. Yes. Due to the flowing electrons.
2. Use the path shown for Ampere’s law. (a
rectangle in the xy plane.) Notice that B is
constant along the vertical sides of the path
because every point on those sides is the same
distance from the sheet.

To see that B has the direction shown,
think of the sheet as a lot of wires, side by side. The fields of the wires
would be as at left. (Right hand rule.) Notice that the horizontal
contributions cancel, leaving you with a field that points up on one side
and down on the other.
E. Ampere's law: B(length of loop) = μo(total current through the loop)
Because of the cable's circular symmetry, use a circle centered on the center of
the cable, for the loop. Since every point on this loop is in an identical situation

 
to every other point, B is the same all along it. This makes B ds reduce to
 
just B s . The cosine factor in the dot product equals 1 in this case.
B(2πr) = μo(total current through the loop)
To find the field at point a, use a circle which goes through point a:
B(2π)(.001 m) = (4π x 10-7)(1.00 A)
(Only count the 1.00 A which is inside the loop.)
B = .0002 T, or 200 μT ans.
Direction: Point right thumb along the current, out of the page.
Your fingers, as they go past point a, point toward the top of the
page.
To find the field at point b, use a larger circle which goes through point b:
B(2π)(.003 m) = (4π x 10-7)(2.00 A)
(With one amp coming out of the page, and three going in, that's a
net current of 2 amps, into the page, through this path. I won't
worry about the current's direction for a minute, until I'm figuring
out the field's direction.)
B = .000133 T, or 133 μT ans.
Direction: Point right thumb along the net current, into the page. Your fingers,
as they go past point b, point toward the bottom of the page.
F. 1.
2.