A toroid has average radius R, winding diameter R , a total of N windings with current I. We "idealize" this as a surface
current running around the surface. What is K? A) I/R B) I/(2 R) C) NI/R D) NI/(2 R)
E) Something else
MD12-1
The magnitude of the magnetic field inside a torus is
A)constant, independent of position within the torusB) non-constant, depends on position within torus
A torus has N windings and current I.
Answer using Ampere's Law :
MD12-2
The vector potential in a certain region is given by
(C is a positive constant) Consider the imaginary loop shown. What can you say about the magnetic field in this region?
A. B is zeroB. B is non-zero, parallel to z-axisC. B is non-zero, parallel to y-axisD. B is non-zero, parallel to x-axis
ˆA(x, y) C y x
5.19
x
y
A
2A 0
J
In Cartesian coordinates, this means:, etc.
Does it also mean, in spherical coordinates, that
?
2Ax 0Jx
2Ar 0J r
A) YesB) No
5.25
A (
r )
0
4
J (r')
d '
Can you calculate that integral using spherical coordinates?
A) Yes, no problemB) Yes, r' can be in spherical, but J still needs to be in
Cartesian components
C) No.
5.25b
The vector potential A due to a long straight wire with current I along the z-axis is in the direction parallel to:
z
I A = ?
ˆA) z
ˆB) (azimuthal)
ˆC) s (radial)
MD12-3
A circular wire carries current I in the xy plane. What can you say about the vector potential A at the points shown?
x
y
z
a
b
IAt point b, the vector potential A is:A) ZeroB) Parallel to x-axisC) Parallel to y-axisD) Parallel to z-axis
At point a, the vector potential A is:A) ZeroB) Parallel to x-axisC) Parallel to y-axisD) Parallel to z-axis
MD12-4a,b
From Purcell,Electricity and Magnetism
E-field aroundelectric dipole
B-field aroundmagnetic dipole(current loop)
Two magnetic dipoles m1 and m2 are oriented in three different ways.
m1 m2
1.
2.
3.
Which ways produce a dipole field at large distances?
A) None of these
B) All three
C) 1 only
D) 1 and 2 only
E) 1 and 3 only
MD12-5
This is the formula from Griffiths for a magnetic dipole at the origin is:
02
ˆ ˆm r(r)
4 r
A
A) It's exact
B) It's exact if |r| > radius of the ring
C) It's approximate, valid for large r
D) It's approximate, valid for small r
Is this the exact vector potential for a flat ring of current with m=Ia, or is it approximate?
5.29
A) The current density J
B) The magnetic field B
C) The magnetic flux B
D) It's none of the above, but is something simple
and concrete
E) It has no particular physical interpretation at all
5.26
dlA
What is ?
In the plane of a magnetic dipole, with magnetic moment m (out), the vector potential A looks like kinda like this
with A ~ 1/r2
x
At point x, which way does curl(B) point?A)Right B)LeftC)InD)OutE)Curl is zero
MD12-6
In general, which of the following are continuous as you move past a boundary?
5.28b
A) A B) Not all of A, just Aperp
C) Not all of A, just A||
D) Nothing is guaranteed to be continuous regarding A
Suppose A is azimuthal, given by
What can you say about curl(A)?
A
c
sˆ
A) curl(A)=0 everywhere
B) curl(A) = 0 everywhere except at s=0.
C) curl(A) is nonzero everywhere
D) ???
5.27
F I L B
The force on a segment of wire L is
B
y
z I(in)
I(out)
x
y
z
B
I
A current-carrying wire loop is in a constant magnetic field B = B z_hat as shown. What is the direction of the torque on the loop?A) Zero B) +x C) +y D) +zE) None of these
MD12-7
Griffiths argues that the torque on a magnetic dipole in a B field is:
m
B
6.1
How will a small current loop line up if the B field points uniformly up the page?
A)
B)
C) D)
m
m
m m
Griffiths argues that the force on a magnetic dipole in a B field is:
( )F m B
If the dipole m points in the z direction, what can you say about B if I tell you the force is in the x direction?
A) B simply points in the x directionB) Bz must depend on xC) Bz must depend on zD) Bx must depend on xE) Bx must depend on z
6.2