(B_Fields– 01)
A proton (charge +e) sits at rest in a uniform magnetic field,
B, that points to the right.
A:
B: Into the page.
C: 0 (no force)
D: Something else, not sure...
Answer: F = qv B. If you're at rest, you feel ZERO magnetic force!

(B_Fields -02)
Two facts about bar magnets:
1) North poles are attracted to South poles (opposites attract)
2) B field lines always point from "N" towards "S".
Compass needles are themselves little bar magnets.
They line up, as shown, pointing in the same direction as the B field lines.
N S
I) The arrow (tip) of a compass needle must be magnetically
A: North B: South
Answer: North: opposites attract!
II) Compass needles point roughly towards the geographic
North Pole of the earth . The earth itself can be viewed as having a giant dipole magnet (much like the one shown above) embedded in it. From the above, which can you conclude?
A: Geographic North = magnetic North Pole of earth
B: Geographic North = magnetic South Pole of earth
Answer: Looking at this picture, apparently geographic north is magnetic south. Curious!
It just has to do with naming conventions, really. The NORTH pole of the COMPASS needle points towards geographic North!

(B_Fields -03)
A negative particle and a positive particle are moving with certain velocities in a constant, uniform magnetic field shown. The direction of the B-field is to the right.
, as
The (+) particle is moving directly left; the (-) particle is moving directly up.
B
(Define "in" = into page,
"out" = out of page).
+
I) The force on the positive particle is...
A: in
B: out
C: zero
D: right
E: left
Answer: Zero, because velocity is (anti)parallel to B. The cross product v x B is zero.
II) What is the force on the negative particle?
Answer: Out of the page. Note that v x B is INTO the page (use the right hand rule - if you can't do this, ask! Point your fingers along v, hold your hand so you can "curl" your fingers towards B, and then holding your thumb straight out, it should point into the page. ) The force is q times this, and since the electron is negative, that reverses the direction of force.

(B_Fields -04):
E constant, uniform magnetic field r
B
€ r
E , and a
. The electric field points up and the magnetic field points out of the page in the diagram below. Which path will the positive particle follow?
€
A B C
A
A A
B (out)
+
D:
DOES
NOT MOVE
Answer: The E field will always start to accelerate a positive charged
particle up the page. But as it begins to move up, v x B will begin to act (use the right hand rule for yourself!) to the right, which means C is the correct answer.
For you to think about: what happens next? What does the curve look like if you "extend" it?

(B_Fields -05).
A (+) charged particle with an initial speed v o
is moving in a plane perpendicular to a uniform magnetic field (B into the page). There is a tenuous gas throughout the region that causes viscous drag and slows the particle over time.
I)The path of the particle is ...
A: a spiral inward B: a spiral outward
B
C: something else/don't know
Answer: The text (and notes) work out the equation r = mv/qB for a particle moving in a circular orbit in a B field. If v is getting slower, then r must be getting smaller, we'll spiral in.
II) If the time for the particle to complete the first revolution
(once around) is 1 sec, the time for the first 5 revolutions is
A: > 5 s B: < 5 s C: 5 s
Answer: The cyclotron frequency (inverse of the time for one revolution) is worked out in your text - it depends on q and B, but NOT on v or R. It will stay the same, so 5 seconds should be right! (You're going slower, but also have less distance to travel, so those two effects actually cancel out)

(B_Fields -06):
A current I flows in a wire sitting in a B field.
I and B are 45 degrees apart.
Both are in the plane of the page.
What is the direction of the force on the wire?
I
A:
45
B
B:
C:
D:
E: None of these, something else, don’t know...
Answer: More practice with the right hand rule. I L x B points INTO the page in this picture. (Point your fingers along the I direction, orient your hand so you can comfortable curly your fingers towards B.
Even though it's not 90 degrees, the directions are still determined. When I do that, my thumb points
INTO the page. That's symbolized as an "X" (like, buried treasure, UNDER the page!)

(B_Fields -07):
A square current loop of length L on each side carries a current, I, in a counter-clockwise direction. It is placed in a uniform B field that points OUT of the page.
I.) What is the magnitude of the net force on the loop?
B
I
L
A: ILB B: 4 ILB
C: zero D: something else E: 2 ILB
Answer: Use the right hand rule on each side. Try it! The right side feels a force to the right, the top side feels a force up the page, and so on. The net force is ZERO, they cancel in pairs. There's some tension in the square, though.
II) The same loop is now in a non-uniform field. where B = B(y) = Ay (A is a constant.) r
B = z ,
The direction of the net force is ...
B stronger
A:
D:
B:
E
: Net force is zero
B weaker
C
:
Answer: Now the force on the top wins, so the net force is up. Kind of like a dipole in an E field - if the field is uniform, there's no net force, but if the field changes, you tend to get pulled towards where the field is stronger!

(B_Fields -08):
A square current loop of length L on each side carries a current, I, in a counter-clockwise direction. It is placed in a uniform B field that points OUT of the page. However, the B field is "cut off" halfway up the current loop, as shown.
I) What is the magnitude of the net force on the loop?
A: ILB L
B: 2 ILB
C: 4 ILB
I
D: zero
E: something else
B
Answer: The bottom segment feels a downward force (convince yourself, use the right hand rule!) which is ILB. That's it. (The two bottom halves of the left and right sides cancel)
II) What is the direction of the net force on the loop?
A: Up
B: Down
C: Out of page
D: Into page
E: Something else
Answer: We just argued: down. You suck this loop into the B field.
What would happen if I went the other way?

(B_Fields -09)
A particle with unknown (but non-zero) charge q moves left with speed v. It enters a region where there is a uniform electric field down and a uniform magnetic field out of the page. The particle is observed to go in a straight line.
B I) The charge of the particle must be ...
A: positive
B: negative
C: not enough information/don't know.
v
Answer: You can't tell! v x B is up the page, E is down the page. So no matter what the sign of q is, F(electric) = q E
E and F(magnetic) = q v x B will always be opposite each other!
II) Suppose the particle is a proton. If the speed of the proton is increased, it will
A: still undergo no deflection
B: deflect out of the plane of the page
C: stay in the plane of the page and deflect upward
D: stay in the plane of the page and deflect downward
E: None of these/not sure.
Answer: The magnetic forced (up the page) will get stronger, since it depends on v. So C is correct.

(B_Fields -10):
A current-carrying loop of wire can pivot on a frictionless axis through its center as shown. There is a uniform magnetic field
B pointing right.
I) How does the loop tend to move?
A: Whole loop simply shifts
(moves) to the right.
B: Loop twists , the right edge I comes towards you.
C: Loop twists , the left edge comes towards you.
D: Nothing at all happens, no torques, no forces.
axis
Answer: More right hand rule practice. I get the force on the right side is INTO the page, on the left side is OUT of the page, on the top and bottom is ZERO. So there's a net torque, pulling the left edge towards you.
B
II) What is the direction of the torque (about the axis of rotation)? (Recall that torque )
A: into page B: out of page
C: up ↑ D: right →
E: torque is zero/don't know
Answer: The convention is that you curl your fingers the way the thing wants to twist, and your thumb points in the direction of torque. In this case, it's up the page. (You can also think about r x F for the two sides - try it out, BOTH should be up the page!!)

(B_Fields -11):
S
A bar magnet is placed near a square loop of wire carrying a current I, as shown. The magnet is perpendicular to the plane of the loop. The loop can rotate freely about the axis.
axis axis coil
Far edge
I into page
B
Near edge,
I out of page
N
I
Magnet
N
Top View
Near edge
S
Pink Yellow
B
The loop tends to rotate so that the near edge (diagram left) moves:
A: to the left
B: to the right
C: The net torque on the loop is zero, so it does not tend to move.
D: None of these/not sure
Answer: Looks to me like NO torque in this particular orientation. If the field had no "spreading out" then the force on the two edges would both be straight towards the center axis. Even with the spreading out, it's symmetric, and I claim there's still no net torque. Convince yourself!

(B_Fields -12)
A permanent bar magnet is broken in half. The two pieces are interchanged, keeping their orientations fixed, as shown below. Do the pieces attract or repel?
A: Attract
B: Repel
A
C: The broken pieces are not magnetic
C
D: Can’t tell
Answer: If we started off, say, N.................S
then when we break we'll have N....S N...S
So when you flip them, A is N, and D is S, and they attract!
B C
D A B
D

(B_Fields -13)
A bar magnet is placed near a rectangular loop of wire carrying a current I, as shown. The loop can rotate freely about the axis. (Shown dashed)
S N I
How does the loop tend to move?
A: Whole loop simply shifts (moves) to the right.
B: Loop twists , the right edge comes towards you.
C: Loop twists , the left edge comes towards you.
D: Nothing at all happens, no torques, no forces.
Answer: The B field points, basically, AWAY from the N, to the right in the page. So the nearby wire feels a force out of the page, and the righthand (farther away) wire feels a force into the page which makes a torque with the left edge coming towards you.