A point charge is fixed at the origin

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

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. (i) Deduce the sign of

q_2

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

q_2

. (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

. (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.