Here are the key steps to solve this problem: 1) The electron is accelerated through 1 kV, so its kinetic energy is 1 keV = 1/2 * m_e * v^2. Solve for v. 2) In the region between the plates, the electric force F_E = qE and magnetic force F_B = qvB. For straight line motion, these forces must balance so F_E = F_B. 3) Set the two force expressions equal and solve for B. 4) Plug in the given values of q = -e, E = 100 V/20mm, and v calculated in step 1. 5) The required uniform magnetic

1. Magnetic force
Dr Ehab Hegazy
Magnetic field
Dr. Ehab Hegazy

3. Earth’s Magnetic Field
•The source of the Earth’s magnetic field
is likely convection currents in the Earth’s
core.
•There is strong evidence that the
magnitude of a planet’s magnetic field is
related to its rate of rotation.
•The direction of the Earth’s magnetic
field reverses periodically.

5. October 31, 2007
Electric Field & Magnetic Field
 Electric forces acting at a distance
through electric field.
 Vector field, E.
 Source: electric charge.
 Positive charge (+) and negative
charge (-).
 Opposite charges attract, like
charges repel.
 Electric field lines visualizing the
direction and magnitude of E.
 Magnetic forces acting at a
distance through Magnetic field.
 Vector field, B
 Source: moving electric charge
(current or magnetic substance,
such as permanent magnet).
 North pole (N) and south pole (S)
 Opposite poles attract, like poles
repel.
 Magnetic field lines visualizing the
direction and magnitude of B.

11. Direction: Right-Hand
Alternative to Rule #1
The force on a positive charge extends
outward from the palm.
The advantage of this rule is that the
force on the charge is in the direction
you would push on something with your
hand.
The force on a negative charge is in the
opposite direction.

24. Velocity Selector
Used when all the particles need to
move with the same velocity.
A uniform electric field is perpendicular
to a uniform magnetic field.
When the force due to the electric field
is equal but opposite to the force due to
the magnetic field, the particle moves in
a straight line.
This occurs for velocities of value.
v = E / B

25. Mass Spectrometer
A mass spectrometer separates ions
according to their mass-to-charge ratio.
In one design, a beam of ions passes
through a velocity selector and enters a
second magnetic field.
After entering the second magnetic
field, the ions move in a semicircle of
radius r before striking a detector at P.
If the ions are positively charged, they
deflect to the left.
If the ions are negatively charged, they
deflect to the right.

26. Example
 A proton is released from rest at a point which is located next to the
positive plate of a parallel plate capacitor.
 The proton then accelerates toward the negative plate, leaving the plate
through a small hole in the capacitor. The electric potential of the
positive plate is 2100 V greater than the negative plate.
 Once outside of the capacitor, the proton encounters a magnetic field
of 0.10 T. The velocity is perpendicular to the magnetic field.
 Find the speed of the proton when it leaves the capacitor, and the
radius of the circular path on which the proton moves in the magnetic
field.

27. Solution
 The only force that acts on the proton while it is
between the capacitor plates is the conservative
electric force. Thus:
ffoo qVmvqVmv  22
2
1
2
1

28. Solution cont.
 If we note that the initial
velocity is zero and that the
charge of the proton is equal
in magnitude to that of the
electron we can write the
following:
)(
2
1 2
fof VVemv 

29. Solution cont.
 Solving for the speed we get:
 
  
smv
kg
VC
mVVe
v
f
fo
f
/103.6
1067.1
2100106.12
/2
5
27
19





 


30. Solution cont.
 When the proton moves in the magnetic field, the
radius of the circular path is:
  
  
mr
TC
smkg
eB
mv
r
f
2
19
527
106.6
10.01060.1
/103.61067.1








31. Charged Particles Moving in Electric and Magnetic Fields
In many applications, charged particles will move in the presence of both
magnetic and electric fields.
In that case, the total force is the sum of the forces due to the individual fields.
 The total force is called the Lorentz force.
In general:
q q  F E v B
r r rr

32. Velocity Selector, cont.
Only those particles with the given speed will pass through the two fields
undeflected.
The magnetic force exerted on particles moving at a speed greater than this is
stronger than the electric field and the particles will be deflected to the left.
Those moving more slowly will be deflected to the right.

33. Example: If a proton moves in a circle of radius 21 cm perpendicular to a
B field of 0.4 T, what is the speed of the proton and the frequency of
motion?
v
r
x x
x x
1
m
qB
f
2

kg
TC
f 27
19
1067.12
4.0106.1






HzHzf 68
101.610
67.128.6
4.06.1




Hzf 6
101.6 
2
m
qBr
v 
kg
mTC
v 27
19
1067.1
21.04.0106.1





s
m
s
m
v 68
101.810
67.1
21.04.06.1



s
m
v 6
101.8 

36. An electron is accelerated through a potential difference of 1.0 kV and directed
into a region between two parallel plates separated by 20 mm with a potential
difference of 100 V between them. The electron is moving perpendicular to the
electric field of the plates when it enters the region between the plates. What
uniform magnetic field, applied perpendicular to both the electron
path and the electric field, will allow the electron to travel in a straight line