1. 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. III. The Lorentz Force Law - + -e v a)Characterize F E : F = eE = constant Directed downward. E

2. 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. III. The Lorentz Force Law - + -e v Constant v Quantitatively?

3. 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? III. The Lorentz Force Law - + -e a = F/m = -eE/m v f = -(2a  y) 1/2 K f = 1/2mv f 2. E +y

4. 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 10 5 m/s. What is the direction of the magnetic field? III. The Lorentz Force Law F B = 10 -14 N = evB(sin  );  = arcsin(10 -14 N/{(1.6 x10 -19 C)(10 5 m/s)(1 T)});  = 39 o w.r.t. the x-axis, but negative charge:  = -39 o.

5. B.Magnetism III. 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 FBFB v FBFB F B = qvB = mv 2 /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)

6. C.The Lorentz Force III. The Lorentz Force Law 1.We can combine electric and magnetic effects by writing a single force law with Electric and Magnetic Fields: F L = q(E + v × B).(III.C.1)