In the rectangle in the drawing, a charge is to be placed at the empty corner to

Question

In the rectangle in the drawing, a charge is to be placed at the empty corner to make the net force on the charge at corner A point along the vertical direction. What charge (magnitude and algebraic sign) must be placed at the empty corner?

http://www.webassign.net/cj8/18-p-025.gif

In the rectangle in the drawing, a charge is to be placed at the empty corner to make the net force on the charge at corner A point along the vertical direction. What charge (magnitude and algebraic sign) must be placed at the empty corner?

Explanation / Answer

The added charge must create a force equal and opposite to that caused by the 3?C charge in the lower rt corner

this force = k*q1*q2/( 4d)^2

The horizonatl component of the added charge = k*q1*Q/(d^2 + 16d^2) *cos(45)
= k*q1*Q*cos(45)/17d^2

Therefore k*q1*q2/16d^2 = k*q1*Q*cos(45)/17d^2

Simplifying = get q2/16 = Q*cos(45)/17

So Q = 17/(16*cos(45))*q2 = 17/(16*cos(45))*3?C = 4.5?C and since is must be attractive to balance the charge Q = -4.5?C

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