The drawing shows four arrangements of two point charges. In each arrangement co

Question

The drawing shows four arrangements of two point charges. In each arrangement consider the total electric potential that the charges produce at location P. Rank the arrangements (largest to smallest) according to the total potential.

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four The drawing shows to the total potential. arrangements of two point charges. In each arrangement consider the total electric pote 2ro 2ro 2ro 2ro 2ro ro ro P +24 +2q 2q P24 B, C, A and D (a tie) A and C (a tie), B, D C, D, A, B D, C, A, B Click if you would like to Show Work for this question: Open Show Work SHOW HINT LINK TO TEXT

Explanation / Answer

potential due to a point charge V = k*q/r

(A)

q1 = -q

q2 = 2q

potential due to q1 , v1 = k*q1/r1 = -k*q/r0

potential due to q2 , v2 = k*q2/r2 = k*2q/(2r0) = k*q/r0

total potential Vtotal = v1 + v2 = 0

(B)

potential due to q1 , v1 = k*q1/r1 = -k*q/(2r0)

potential due to q2 , v2 = k*q2/r2 = k*2q/(r0) = 2*k*q/r0

total potential Vtotal = v1 + v2 = (k*q/r0)*(2-1/2) = (3/2)*(k*q/r0)

(C)

potential due to q1 , v1 = k*q1/r1 = -k*q/(2r0)

potential due to q2 , v2 = k*q2/r2 = k*2q/(2r0) = k*q/r0

total potential Vtotal = v1 + v2 = (k*q/r0)*(1 -1/2) = (1/2)*k*q/r0

(D)

potential due to q1 , v1 = k*q1/r1 = -k*q/r0

potential due to q2 , v2 = k*q2/r2 = k*2q/(2r0) = k*q/r0

total potential Vtotal = v1 + v2 = 0

B > C > A = D

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