Download The magnetic force law (Lorentz law)

The magnetic force law (Lorentz law)
The magnitude of the force is
the B field x the perpendicular velocity x charge
Or
The velocity x the perpendicular B field x charge

 
F  qv  B

F  q vB sin 
Use right hand rule, but be careful … notice sign of charge!
Another way to take a cross product
i¦
v v
A  B  Ax
¦j
Ay
¦k
Az
Bx
By
Bz
We discussed the flux of the magnetic field last time.
Through any closed surface, it’s zero.
 
 B  dA  0
No “sources” (origins)
for magnetic field lines.
We will see in the coming month that magnetic flux through
open surfaces IS important. It’s calculated the same way we
calculated flux of the electric field…
A B field of 10 Tesla (T) is pointing north and up
(30° above horizontal.)
What is the flux of the B field through the desk, A= 2 m2 ?
Recall cos(30°) = √3/2
cos(60°) = 1/2
A] 5 Tm2
B] 5√3 Tm2
C] 10 Tm2
D] 10√3 Tm2
E] 20 Tm2
As the magnetic force is always perpendicular to
velocity, a uniform B field cannot cause particles to
speed up or slow down.
It just makes them go in circles.
(OR HELICES)
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)
Magnetic forces on current carrying wires.
Current means charges in motion. The field exerts a force on the
moving charge carriers. They transfer that force to the lattice
through collisions.
F I l B
wire
F qv B
charge
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.)
velocity
Use A for i), B for ii) etc.
Same speed. Ans C (iii)
A curious point: since magnetic forces are perpendicular to velocity,
they do no work on charges.
But they do work on wires!
How can this be?
(I’m not going to tell you the answer…life should have some mysteries, eh?)
F I l B
wire
F qv B
charge
Hall Effect -- How to determine the sign of charge carriers
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?
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
Why do compass needles align with B?
Why do opposite poles attract?
Why do magnets attract iron?
 
  B


  IA
 
U    B

Magnetic Torque on a current loop
Magnetic Moment
Potential energy of a current loop
Sources of Magnetic Fields - Moving Charges
Biot-Savart Law
1/r2 dependence in a given direction
No B field front or back
B field “curls” around charge trajectory
0 is a constant, just like 0 for E fields. “Permeability of space”
Sources of Magnetic Fields - Moving Charges
Biot-Savart Law
A charge moves in a circle at constant speed.
At the time shown, where is B=0?
Or choose E: at more than one point shown
Sources of Magnetic Fields - Moving Charges
Biot-Savart Law
A charge moves in a circle at constant speed.

If one wishes to calculate the B field at point D, what is r
A) A unit vector upward B) a unit vector downward
?
Sources of Magnetic Fields - Moving Charges
Biot-Savart Law
A + charge moves in a circle at constant speed.
What is the direction of the B field at D?
A] left
B] into page
C] out of page D] down E] up
Sources of Magnetic Fields - Moving Charges
Biot-Savart Law
A + charge moves in a circle at constant speed.
What is the direction of the E field at D?
A] left
B] into page
C] out of page D] down E] up
Sources of Magnetic Fields - Moving Charges
Biot-Savart Law
A + charge moves in a circle at constant speed.
What is the direction of the B field at point B?
A] out of page B] out of page and up
C] out of page and up and right
Sources of Magnetic Fields - Moving Charges
Biot-Savart Law
What is the ratio of the B field strength at C to that at D?
A] BC/BD=4
B] BC/BD=2
C] BC/BD=1
D] BC/BD=1/4
Sources of Magnetic Fields - Moving Charges
Biot-Savart Law
The “pièce de résistance!” What is the ratio of the B field strength at C to
the strength at B?
A] BC/BB=4
B] BC/BB=2√2
C] BC/BB=2
D] BC/BB= BC/BD=√2
Just as with force laws,
I l  q v
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


Now let’s work out the contribution from the semicircle.