Identical point charges of +1.6 C are fixed to diagonally opposite corners of a

ID: 1432095 • Letter: I

Question

Identical point charges of +1.6 C are fixed to diagonally opposite corners of a square. A third charge is then fixed at the center of the square, such that it causes the potentials at the empty corners to change signs without changing magnitudes. Find the sign and magnitude of the third charge. (Answer must be in C and please no rounding) Identical point charges of +1.6 C are fixed to diagonally opposite corners of a square. A third charge is then fixed at the center of the square, such that it causes the potentials at the empty corners to change signs without changing magnitudes. Find the sign and magnitude of the third charge. (Answer must be in C and please no rounding)

Explanation / Answer

Here,

identical charge , q = 1.6 uC

let the side of square is d

initially , the potential at the empty corner is V

V1 = 2 k * q/d

after placing the third charge

potential at the corner is Q

V2 = 2k*q/d + k * Q/(sqrt(2) * d/2)

as V1 = - V2

- 2 k * q/d = 2k*q/d + k * Q/(sqrt(2) * d/2)

4 * k* q/d = - k * Q* sqrt(2)/d

- 4 * q = sqrt(2) * Q

Q = -4 * 1.6/sqrt(2)

Q = -4.52 uC

the magnitude and sign of third charge is -4.52 uC

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Identical point charges of +1.6 C are fixed to diagonally opposite corners of a

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