Question

Two point charges q and -4q are kept d distance apart .Find the distance of the point from the charge q on the line joining the two charges at which the potential due to the system be zero will there be more such points

Answer 1

Two point charges q and -4q are kept d distance apart. we have to find the distance of the point from the charge q on the line joining the two charges at which the potential due to the system be zero.

Let x distance from the charge q on the line joining the two charges at which the potential due to the system be zero.

so, potential due to q at point = Kq/x

potential due to -4q at point = k(-4q)/(d - x)

now, net potential at that point = kq/x + k(-4q)/(d - x) = 0

or, kq/x - 4kq/(d - x) = 0

or, kq/x = 4kq/(d - x)

or, 1/x = 4/(d - x)

or, d - x = 4x

or, x = d/5

hence, at d/5 distance from the charge q , potential of the system will be zero.

yes of course there will be more such points.

let at point A ( left side of charge q, doesn't lie between the q and -4q ) , potential of system be zero.

then, potential due to q = kq/x

and potential due to -4q = -4kq/(d + x)

so, potential of the system = kq/x - 4kq/(x + d) = 0

or, kq/x = 4kq/(d + x)

or, d + x = 4x

or, x = d/3 , hence at d/3 distance from the charge q( left side of charge q) potential of system will be zero.