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III. The Lorentz Force Law
A. Electric Field
2. Field and Force
Example: Consider an electron moving horizontally
a constant speed v between two parallel plates as
shown. The plates are oppositely charged, and
produce a uniform upwardly directed E-field in the
region between the plates. Describe the trajectory
of the electron.
-e
v
+
E
a) Characterize FE:
• F = eE = constant
• Directed downward.
III. The Lorentz Force Law
A. Electric Field
2. Field and Force
Example: Consider an electron moving horizontally
a constant speed v between two parallel plates as
shown. The plates are oppositely charged, and
produce a uniform upwardly directed E-field in the
region between the plates. Describe the trajectory
of the electron.
Constant v
Quantitatively?
-e v -e
-e -e
-e
-e-e
Constant v
-
+
III. The Lorentz Force Law
A. Electric Field
2. Field and Force
Example: Suppose an electron is released from
rest just below the top plate. What is its speed &
kinetic energy when it reaches the bottom plate?
a = F/m = -eE/m
vf = -(2aDy)1/2
Kf = 1/2mvf2.
-e
-e
+y
+
E
III. The Lorentz Force Law
B. Magnetism
4.
Example: An electron is supported against a downward
force with magnitude F = 10-14 N by a uniform magnetic
field with strength B = 1 T. The electron is moving along
the x-axis with a speed of 105 m/s. What is the direction
of the magnetic field?
FB = 10-14 N = evB(sinq);
q = arcsin(10-14 N/{(1.6 x10-19 C)(105 m/s)(1 T)});
q= 39o w.r.t. the x-axis, but negative charge:
q = -39o.
III. The Lorentz Force Law
B. Magnetism
4.
Example: Describe the path of a negative charge
moving in the positive x-direction with constant
speed v in the presence of a uniform magnetic
field pointing in the negative z-direction.
FB
v
FB = qvB = mv2/r;
FB
r = mv/qB;
q/m = v/rB.
v = qrB/m.
w = v/r = |q|B/m.
r
v
(III.B.3)
(III.B.4)
(III.B.5)
(III.B.6)
III. The Lorentz Force Law
C. The Lorentz Force
1.
We can combine electric and magnetic effects by
writing a single force law with Electric and
Magnetic Fields:
FL = q(E + v × B).
(III.C.1)