Download Permanent magnets are just collections of little current loops

Currents cause magnetic fields. If we say that the
compass lines up along the field, then the field curls
around the wire. B field lines have no beginning or end!
Permanent magnets are just
collections of little current loops
In Jules Verne’s story “Journey to the Center of the Earth”,
some dudes travel deep inside the Earth. If this were
possible and they had a compass with them, what direction
would their N compass needle point?
A] toward the Earth’s northern geographic pole
B] toward the Earth’s southern geographic pole
C] it would have no preferred direction
Magnetic field lines curl around currents, forming closed loops.
As such, they have no beginning and no end.
• What is the total flux of the magnetic field through any closed
surface? Recall that
 E  dA  q
enc
 B  dA  ?
A] 0

B] Ienc times a positive constant
C] -Ienc times a positive constant
/0
Note key differences with E fields:
NO force if v=0
NO force if v is parallel to B
Direction of force depends on direction of v (perp to v!)
What is the magnitude of
the magnetic force on the
charge moving with
velocity v3?
What is the magnitude of
the magnetic force on the
charge moving with
velocity v1?
What is the magnitude of
the magnetic force on the
charge moving with
velocity v2?
What is the direction of
the magnetic force on the
charge moving with
velocity v2?
Centripetal force = Fmag
Cyclotron frequency
Part a. Use A for i), B for ii) etc.
Radius is proportional to v. Ans. B
(ii)
Part b. Use A for i), B for ii) etc.
Because r is proportional to v,
the period is unchanged.
Ans. A (i)
velocity
Use A for i), B for ii) etc.
Same speed. Ans C (iii)
F I l B
wire
F qv B
charge
http://www.falstad.com/vector3dm/
Why do compass needles align with B?
Why do opposite poles attract?
Why do magnets attract iron?
The electric potential is
A] higher at A
B] higher at B
C] the same in both places
If the current direction were the same, but electrons
carried the current, where would the electric potential
be higher? B
The unit of the magnetic field B (the Tesla)
A] is the same as the electric field times a velocity
B] is the same as the electric field divided by a velocity
C] cannot be expressed as either of these
(The electric field is V/m.)
What is the sign of the charge carriers in this conductor?
A] +
B] C] Can’t tell
What is the drift velocity of the negative charge carriers?
A] 0
B] 10-3 m/s
C] 10-2 m/s
D] 10-1 m/s
E] 1 m/s
A proton (+) and an electron (-)
move side by side both with
velocity v as shown.
What is the direction of the magnetic field at the electron
due to the proton (in our “laboratory” frame of reference)?
A] into page
B] out of page
C] upward
D] downward
E] to the right
A proton (+) and an electron (-)
move side by side both with
velocity v as shown.
The magnetic field is into the page, by RHR. What is the
direction of the magnetic force on the e- ?
A] into page
B] out of page
C] upward
D] to the left
E] to the right
A proton (+) and an electron (-)
move side by side both with
velocity v as shown.
The magnetic force on the electron is away from the proton.
What direction is the total (electric + magnetic) force on the
electron? (v<c)
A] into page
B] out of page
C] upward
D] to the left
E] to the right
A proton (+) and an electron (-)
move side by side both with
velocity v as shown.
The total force on the electron is still attractive, but weaker
than if no magnetic force were present.
What is the total force on the electron if v=c?
A] 0
B] infinite, away from the proton
C] infinite, toward the proton
A proton (+) and an electron (-)
move side by side both with
velocity v as shown.
The total force on the electron is still attractive, but weaker
than if no magnetic force were present.
What is the total force on the electron if v=c? Ans 0!
Clocks slow to a STOP as v -> c!
This “version” of the right hand rule gives the same
result as v ˆ
Try it.
dl  r
What is the contribution of the straight
sections of the wire to the magnetic field in
the center of the semicircle?
A] Each contributes 0


B] They both have contributions that are
opposite, and so add to 0
C] Each contributes
0 I
2R
D] infinite




Point P is a perpendicular distance x from each wire.
Both wires carry current I in the direction shown.
What is the magnetic field at P?
A] 0
0 I
B]
2x
0 I
C]
x
D] Insufficient information
B=0 iii
Currents out of plane
attractive
In Ampere’s law, Gauss’ law, etc. :
If we let loops and surfaces get infinitesimally small, we get
relationships for derivatives of the fields.
There are four relationships, called “Maxwell’s Equations”
 B  dl   I
0
   B  0 J
E 0
 B  dA  0 
B 0
  E   / 0
These are what we (in physics 161) know now. They are
still incomplete: we will fix them in the remaining weeks.

Maxwell’s Equations (corrected)
E
  B  0 J  00
t
B
E 
t
B 0
  E   / 0
Nothing would demonstrate your love of, and dedication
to physics like a….
Maxwell Equations Tattoo !
  B  0 J  00
E 
E
t
B
t
B 0
  E   / 0

And… they look great on chicks as well as dudes…