A point charge q1 = -2.0 C is at the origin, and a second point charge q2 = +5.4

Question

A point charge q1 = -2.0 C is at the origin, and a second point charge q2 = +5.4 C is at the point x = 1.3 m, y = 3.0 m.
(a) Find the x and y coordinates of the position at which an electron would be in equilibrium.
x = m
y = m

(b) Find the x and y coordinates of the position at which a proton would be in equilibrium.
x = m
y = m

(c) Suppose the charges q1 and q2 were both doubled. How would your answers change?
The electron would be in equilibrium at the following point.
x = m
y = m

The proton would be in equilibrium at the following point.
x = m
y = m

Why?

Explanation / Answer

at the point of equilibrium

the forces on the electron should be equal and opposite in direction

for part a

let at point x=x there will be equilibrium

this point will be outside the line joining the charges .because in between the charges there will be no equilibrium since the charges opposite in sign.

the forces on the electron will be equal in magnitude and opposite in direction

hence

k*2*q/x*x=k*5.4*q/(x-1.3)*(x-1.3)

solving x=-2.02m

similarly for y coordinate

k*2*q/y*y=k*5.4*q/(y-3)*(y-3)

solving y=-4.665m

part b

for proton also the x and y points for equilibrium will remain same

so x=-2.02m y=-4.665m

part C

even now the x and y coordinates remains same

because the ratio of chrages remain same as before.

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