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III. The Lorentz Force Law

III. The Lorentz Force Law. Electric Field Field and Force

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III. The Lorentz Force Law

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  1. III. The Lorentz Force Law • Electric Field • 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. - • Characterize FE: • F = eE = constant • Directed downward. v E -e +

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

  3. III. The Lorentz Force Law • Electric Field • 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. +y - -e E -e +

  4. III. The Lorentz Force Law B. Magnetism • 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)}); • = 39o w.r.t. the x-axis, but negative charge: • = -39o.

  5. III. The Lorentz Force Law B. Magnetism • 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 FB = qvB = mv2/r; r = mv/qB; (III.B.3) q/m = v/rB. (III.B.4) v = qrB/m. (III.B.5) w = v/r = |q|B/m. (III.B.6) v FB FB v

  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)

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