Question

Two point charges Q and q are placed at a distance X and x/2 from a third charge of 4q. Calculate the magnitude and nature of Q such that net force experienced by q is 0

Answer 1

Two point charges Q and q are placed at a distance X and x/2 from a third charge of 4q.

see figure,

here it is clear that, if distance between Q and 4q is x then, distance between Q and q is (x - x/2) = x/2

a/c to question,

net force experienced by q = 0

force exerted by Q on q + force exerted by 4q on q = 0

or, kQq/(x/2)² (rightward) +  kq(4q)/(x/2)²(leftward) = 0

or, kQq/(x/2)² (rightward) - 4kq²/(x/2)²(rightward) = 0

or, kQq/(x/2)² = 4kq²/(x/2)²

or, Q = 4q

hence, magnitude of Q = 4q and nature of Q is same as q or 4q.