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Multiple Choice
An electron moves from point A to point B. The potential difference between these two points is 100 V. What is a. the point of higher potential? b. the work done on the electron? c. the final speed of the electron if its initial speed is zero?
A
(a) B (b) 1.6 × 10-17 J (c) 5.95 × 106 m/s
B
(a) B (b) -1.6 × 10-17 J (c) 5.95 × 106 m/s
C
(a) A (b) 1.6 × 10-17 J (c) 5.95 × 106 m/s
D
(a) A (b) -1.6 × 10-17 J (c) 5.95 × 106 m/s
Verified step by step guidance
1
Identify the direction of electron movement: Electrons move from a region of lower potential to a region of higher potential. Therefore, if the electron moves from point A to point B, point B is at a higher potential.
Calculate the work done on the electron: Use the formula for work done by an electric field, which is W = q * V, where q is the charge of the electron (-1.6 × 10^-19 C) and V is the potential difference (100 V).
Determine the sign of the work done: Since the electron is negatively charged, the work done on it by the electric field is negative, indicating that the field does work on the electron.
Use the work-energy principle to find the final speed: The work done on the electron is equal to the change in kinetic energy, W = ΔK = 0.5 * m * v^2 - 0.5 * m * u^2, where m is the mass of the electron (9.11 × 10^-31 kg), v is the final speed, and u is the initial speed (0 m/s).
Solve for the final speed: Rearrange the equation to solve for v, the final speed of the electron, using the known values for work done and the mass of the electron.