The four cases below all show a ball with a charge of -3q at the top right corne

Question

The four cases below all show a ball with a charge of -3q at the top right corner of a square. Then there is either one, two, or three additional charged balls, each ball located at a different corner of the square. Note that the electric potential is defined to be zero an infinite distance from the charges. For parts (b) and (c), use q-6.80 x 10-6 C, and L-30.0 cm, as well as k = 9.00 x 109 N·m2/C2. -2q (a) Rank the cases based on the electric potential at the center of the square, from most positive to most negative. (Use only "S" or "=" symbols. Do not include any parentheses around the letters or symbols.) (b) In case c, calculate the electric potential at the center of the square (c) In case C, calculate the electric potential at the bottom left corner of the square.

Explanation / Answer

distance from center to vertex r = L/sqrt2 = 21.2 cm = 0.212 m

potential at the center

VA = k*(q-3q)/r = -2k*q/r

VB = k*(-3q-2q)/r = -5kq/r

Vc = k*(q-3q+q)/r = -kq/r

VD = k*(q-3q+q-2q)/r = -3kq/r

C > A > D > B

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part(b)

Vc = -9*10^9*6.8*10^-6/0.212 = 2.88*10^5 V

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part(c)

Vc = k*q/L + k*q/L - k*3q/(L*sqrt2)

Vc = 9*10^9*6.8*10^-6/0.3 + 9*10^9*6.8*10^-6/0.3 - 9*10^9*3*6.8*10^-6/(0.3*sqrt2)

Vc = -24750 V

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