Question

Two point charges lie on the x axis. A charge of 9.5 μC is at the...

Two point charges lie on the x axis. A charge of 9.5 μC is at the origin, and a charge of -5.3 μC is at x = 10 cm . Part A) At what position x would a third charge q3 be in equilibrium?

Part B) Does your answer to part A depend on whether q3 is positive or negative? Explain. Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

Charge at the origin, q1 = 9.5 x 10-6 C

Second charge, q2 = - 5.3 x 10-6 C

Distance between q1 and q2 is r = 0.10 m

Part A:

There will be a neutral point at a distance x metre to right of q2. The net electric at a neutral point is zero.

At the neutral point, electric field of q1 = electric field of q2 in magnitude

1/4πε0 q1/(r + x )2 = 1/4πε0 q1/x2

9.5/(r + x )2 =5.3/ x2

x2 = (r + x )2 x5.3/9.5

x = ( r + x) x 0.747

x = (0.10 + x ) x 0.747

x = 0.296 m

the net force on a charge q3 placed at the neutral point is zero.

therefore, the third charge q3 will be in equilibrium at a distance X = 0.10 +x = 0.10 + 0.296 = 0.396 m from the origin.

part B:

the answer to the part A is independent of the nature of charge q3 because any type of charge at a neutral point experience ZERO force.

Hence, q3 can either be positive or negative.