Physics

Problem

A point charge

q_1=+6\,\mu\text{C}

is fixed at the origin. Another point charge

q_2

is placed at the point

(0.30\,\text{m},\,0.40\,\text{m},\,0)

in vacuum. The magnitude of the electrostatic force on

q_2

is measured to be

1.20\,\text{N}

and its direction is found to be exactly toward the origin. a. (i) Deduce the sign of

q_2

and justify your answer using the observed direction of the force. b. (ii) Calculate the magnitude of

q_2

. c. (iii) Determine the force

\mathbf F_{12}

q_1

due to

q_2

in unit-vector form and verify that it satisfies Newton’s third law with the force acting on

q_2

. d. (iv) If

q_2

is now moved to the point

(-0.30\,\text{m},\,-0.40\,\text{m},\,0)

while keeping its charge unchanged, predict the new direction of the force on

q_2

and explain your reasoning.

Intuitive explanation

This problem hinges on using Coulomb's law in reverse: you know the force magnitude and direction, so you can solve for the unknown charge $q_2$ . Since the force points toward the origin, $q_2$ must be opposite in sign to $q_1$ (attraction). Calculate the distance from $q_1$ to $q_2$ , then rearrange $F = k|q_1 q_2|/r^2$ to find $q_2$ .

Intuitive explanation

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