2: Three charges are arranged in an equilateral triangle of side 10 m. Clockwise

Question

2: Three charges are arranged in an equilateral triangle of side 10 m. Clockwise from lower left they are 2 nC, -4 nC and 3 nC. a: Determine the voltage at the origin. What does this tell you? b: Determine the electrical potential energy of the system. What does this tell you? c: Imagine that Qs is moved straight vertically upward under the influence of the other two charges and an external force (perhaps an external force provided by you). After moving a short distance, it is again definitely at rest. Does the external force do positive or negative work during this process? Explain. Determine the minimum work required by that external force if Q3 moves a distance of 0.5 × 10-8 m Qi Q2

Explanation / Answer

(A) r1= r2 = D/2 = 5 x 10^-9 m

r3 = sqrt(D^2 - r1^2) = 8.66 x 10^-9 m

V = k Q1 / r1 + k Q2 / r2 + k Q3 / r3

V = 4.84 x 10^9 Volt

(B) PE = k q1 q2 / d + k q2 q3 / d + k q1 q3 / d

PE = - 12.6 J  

PE is negative that means positive work have required to move these charges away from them.

(C) positive work.

PEf = k q1 q2 / d + k q2 q3 / r + k q1 q3 / r

r = sqrt[ 1.366^2 + 0.5^2] x 10^-8 = 1.45 x 10^-8 m

PEf = - 7.01 J

Work done = PEf - PEi

= - 7.01 - (-12.6)

= 5.60 J

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