Question

A point charge of 4.4 icro coulumbs is placed at the origin (x1=0) of a coordinate system, and another charge of -1.9 micro coulumbs is placed on the x axis at x2=.28m.

a)where on the x axis can a third charge be lpaced in meters so that the net force is zero?

b)what if bot charges are positive, that is what if the second charge is 1.9 micro coulums?

Answer 1

both charges are opposite so neutral point will be uotside the charges and is nearer to the charge of smaller magnitude

let distance of neutral point from 1.9 microcoulombs be x m

then distance from 4.4 microC = x + 0.28 m

net electric field = 0 at neutral point

so, 4.4/(0.28+x)² = 1.9/x²

x/x+0.28= 0.657

=> x+0.28/x = 1.52

=> 0.52 = 0.28/x

x = 0.5366 m

coordinate of point = x+0.28 = 0.8166 m

b.) if both charges +

neutral point between the charges and still closer to the smaller charge

similarly

4.4/x^{2 =} 1.9/(0.28-x)²

0.28-x/x=sqrt(1.9/4.4)

x= .1689 m