For the following problems: Do not round up intermediate calculations. Carry the

Question

For the following problems: Do not round up intermediate calculations. Carry the full precision of all values until a final answer. Round up only the final answers to keep four decimal places. 1. Four electrons are held in place at the corners of a square 10 nm (exact) on each side, as shown. Calculate the potertial they set up at point A, the center of the square. Show all your work and explain your reasoning. (Use k = 9.00 × 10, N-m2/C2.) O.0 5. Energy conversions: Electric potential energy can be converted to kinetic energy Consider the case when the alpha particle is brought from infinity to point A. If the alpha particle starts at infinity from rest, calculate how fast it will be moving when it gets to point A.

Explanation / Answer

1.

a = length of side of square = 10 nm

L = length of diagonal = sqrt(2) a = 14.1 nm

r = distance of each corner from the center = L/2 = 14.1/2 = 7.05 nm = 7.05 x 10-9 m

q = charge at each corner = - 1.6 x 10-19 C

electric potential at A is given as

V = k q/r + k q/r + k q/r + k q/r

V = 4 k q/r = 4 (9 x 109) (- 1.6 x 10-19)/(7.05 x 10-9) = - 82 Volts

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