3. Figure 1 shows several points. Voltages are given between several pairs of po

Question

3. Figure 1 shows several points. Voltages are given between several pairs of points, along with a notation convention which will allow you to see which points are at higher potentials than others (for example ?VAD = VA ? VD = ?30V , which tells you that point D is at a higher potential than A).

(a) Find ?VDC.

(b) Where is the potential zero? Explain your answer.

(c) Suppose an electron comes through this region. It passes through point A at a speed of 5.00 × 106 m/s. How fast is it going as it passes through point C?

Explanation / Answer

a)

VDC = Vd - Vc = (Vd - Va) + (Va - Vb) + (Vb - Vc) = - Vad + (- Vba) + (- Vcb) = - (-30) + (- 60) + (- 20) = - 50

c)

VaC = Va - Vb + Vb - Vc = - 60 - 20 = - 80 volts

initial KE + electric potential energy = final KE

(0.5) m Vi2 + q VaC = (0.5) m Vi2

(0.5) (9.1 x 10-31) (5 x 106)2 + (1.6 x 10-19) (80) = (0.5) (9.1 x 10-31) Vf2

Vf = 7.3 x 106 m/s

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