A known positive charge is located at point P, as shown above, bet ween two unknown charges, Q1 and Q2. P is closer to Q2 than to Q1 If the net electric force acting on the charge at P is zero, it may correctly be concluded that
(D) Q1 and Q2 have the same sign, but the magnitude of Q1 is greater than the magnitude of Q2
(E) Q1 and Q2 have the same sign, but the magnitude of Q1 is less than the magni- tude of Q2
The answer is D. Why not E? since P is near Q2 doesnt it mean that the magnitude of Q2 should be greater since magnitude and distance are inversely proportional?
The net force on P is zero, this means the force that results from Q1 acting on P is opposite and equal in magnitude of the force resulting from Q2 acting on P. However Q1 is further away from P. If Q1 and Q2 were charged the same than the force resulting from Q1 on P would be less as force decreases with distance. In order to make up for the greater distance and make the forces equal the Q1’s charge need to be greater than Q2’s charge. This corresponds to answer D.
Similarly, just to get some intuition, imagine Q1 and Q2 were light bulbs and P is the observer. P sees both bulbs as having the same brightness, however Q1 is further away. This can only be true if Q1 's wattage is actually stronger than Q2’s.