Charges are placed on an equilateral triangle (all angles are equal and equal to

Question

Charges are placed on an equilateral triangle (all angles are equal and equal to 60 degrees). The length of each side of the triangle is 9.6 meters. A charge of +7.2 micro-Coulombs is placed at the bottom corner of the triangle and another charge of +7.2 micro-Coulombs is placed in the other corner at the bottom of the triangle. Another charge is placed halfway between the two other charges (directly below the other corner of the triangle - see sketch). What does this charge need to be such that the total electric field in the third, unoccupied corner, of the triangle is equal to zero? Answer in micro-Coulombs.

Explanation / Answer

because of symmetry, the x component of electric field contributed by two 7.2 C charges cancels each other.

y component is

cos30*kq/d^2 + cos30*kq/d^2

assume the 3rd charge is Q, then

kQ/(dcos30)^2 + 2cos30 * kq/d^2 = 0

or

Q/(cos30)^2 + 2cos30q = 0

Q =-2(cos30)^3*q = -2*0.65*7.2 = -9.35 C

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