Question

The point charge q1 (+4 μC) is located at x1= -5.7m, and the point charge q2 (+9 μC) is located at x2 = +14.1m, as shown in the figure. The net electric force on a point charge q3 (+5 μC) is zero at the x-coordinate (in m): K = 9 x 10+9 N.m2.C-2 , ε0 = 8.85 x 10-12 C2.N-1.m-2 Select one: -3.1 +11.0 +2.2 +15.7 -1.2

Answer 1

Charge, q1 = 4μC

Charge, q2 = 9 μC

Distance between the two charges, r = 5.7 + 14.1 = 19.8 m

Let x be the distance of the neutral point from the charge q1 where the net electric field is zero. Then,

Electric field of charge q1 at the neutral point has the same value as that of charge q2

1/4πε_o q1/x² = 1/4πε_o q2/(r – x)²

4/ x² = 9/(r – x)²

2/x = 3/ ( r – x)

( r – x ) = 1.5 x

r = 2.5 x

x = r/2.5 = 19.8/2.5 = 7.9 m

x coordinate of the neutral point = 7.9 – 5.7 = 2.2m

when a charge 5 μC is placed at the neutral point , it experience ZERO force.

The X- coordinate of the point where the force on a charge 5 μC is zero is:

+2.2 m