Three identical point charges are fixed at the vertices

PHYSICS · Subjective · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

Three identical point charges

q = 5\,\mu\text{C}

are fixed at the vertices

A

B

and

C

of an equilateral triangle of side

6\,\text{cm}

that lies in a horizontal plane. The vertex

A

is taken to be at the origin

O(0,0)

, vertex

B

(6\,\text{cm},\,0)

on the positive

x

-axis and vertex

C

(3\,\text{cm},\,3\sqrt{3}\,\text{cm})

. (i) For the charge at

A

, find the magnitude of the force due to the charge at

B

and resolve this force into its

x

and

y

components. (ii) Repeat part (i) for the force on the charge at

A

due to the charge at

C

. (iii) Obtain the algebraic sum of the

x

and

y

components found in parts (i) and (ii) to determine the net force components on the charge at

A

. (iv) Hence compute the magnitude of the net force and the angle it makes with the positive

x

-axis. Give the final numerical results correct to one decimal place.