Two identical point charges each having a charge of q = 48 ?C are aligned horizo

Question

Two identical point charges each having a charge of q = 48 ?C are aligned horizontally and are separated by a distance 2d as shown in the figure above.

What charge Q (in ?C) should be placed at the midpoint of the line connecting the two charges, q such that all of the charges are in equilibrium?

What charge Q (in ?C) should be placed at the midpoint of the line connecting the two charges, q such that all of the charges are in equilibrium? Two identical point charges each having a charge of q = 48 ?C are aligned horizontally and are separated by a distance 2d as shown in the figure above.

Explanation / Answer

The top charge exerts a force on the negative charge (ke*qQ) / ((d/2)^2 + x^2) which is directed upwards and left, at an angle theta. Now notice that the y-components of the charges canel each other out so there is no y-component in the final result. So procceed in finding the x-component of the 2 forces. Rather than doing this twice, because of the symmetry you just need to mulitply the answer by 2. The total force is: -2(ke*qQ) / ((d/2)^2 + x^2)^(1/2) * cos(theta) i

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