Question

A point charge of -1.5 µC is located at the origin. A second point charge of 12 µC is at x = 1 m, y = 0.5 m. Find the x and y coordinates of the position at which an electron would be in equilibrium.

1)

x =

2)

y =

Answer 1

Point where electron is in equilibrium is the point where electric field due to given 2 charges is zero. With two charges in space, field is zero on the line joining two charges and for opposite sign of charges, zero field is on the side of smaller charge in magnitude.

Here smaller charge is at origin and bigger charge is in first quadrant, zero field point is in third quadrant. Let distance of zero field point from origin be 'a', distance of point from 12 C charge is
a + (1² +0.5²)^1/2= a+ 1.12 m
Field due to charges is proportional to q/r²
hence for zero field
1.5/a² = 12/(a+1.12)²
a+1.12 = 2*2^1/2 a
a = 1.12/(2*2^1/2 -1) = 0.61 m
(x² +y²)^1/2 = 0.61
point is on the line y = x/2 and third quadrant
x= -0.544
y=-0.272