Question

two fixed charges +q AND +4q are kept at a distance r from eachother. at what distance between the charges ,a third charge q be placed to keep them in equilibrium.

Answer 1

plz explain more

Answer 2

Let a charge Q be kept at a distance of "x" from the charge 4q.
All the three charges should be in eqbm.
Applying eqbm condition to the Q charge

k(4q)Q/x^2=kQq/(r-x)^2

Solving this we get x=2r/3
Hence charge Q will remain in eqbm if it is kept at 2r/3 from 4q no matter how large Q might be. But in order for the other charges to remain in eqbm we have to find the value of Q.

q will repel 4q. So obviously Q should be negative.Now we find the magnitude of Q by applying eqbm on 4q (u may use q also).

kQ(4q)/(2r/3)^2=4kqq/r^2

we will get Q=4q/9.

*****USE OF q IN APPLYING EQBM WILL ALSO YIELD THE SAME VALUE OF "Q"*****

Answer 3

thanx