A. Electric Field2. 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.

III. The Lorentz Force LawIII. The Lorentz Force Law

-

+-e

va) Characterize FE:

• F = eE = constant• Directed downward.

E

A. Electric Field2. 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.

III. The Lorentz Force LawIII. The Lorentz Force Law

-

+-e v -e -e-e-e

-e-e

Constant v

Constant v

Quantitatively?

A. Electric Field2. 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?

III. The Lorentz Force LawIII. The Lorentz Force Law

-

+

-e

-e

a = F/m = -eE/mvf = -(2ay)1/2

Kf = 1/2mvf2.

E

+y

B. Magnetism4. 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?

III. The Lorentz Force LawIII. The Lorentz Force Law

FB = 10-14 N = evB(sin);

= arcsin(10-14 N/{(1.6 x10-19 C)(105 m/s)(1 T)});= 39o w.r.t. the x-axis, but negative charge:

= -39o.

B. Magnetism

III. The Lorentz Force LawIII. The Lorentz Force Law

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.

r

v

FB

vFB

FB = qvB = mv2/r;

r = mv/qB; (III.B.3)q/m = v/rB. (III.B.4)v = qrB/m. (III.B.5) = v/r = |q|B/m. (III.B.6)

C. The Lorentz Force

III. The Lorentz Force LawIII. The Lorentz Force Law

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)