Three point charges are placed at the corners of a right-angled isosceles triangle…

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

Problem

Three point charges are placed at the corners of a right-angled isosceles triangle that lies in the

xy

-plane. Charge

Q_1 = +q

is at the origin

O(0,0)

, charge

Q_2 = +q

is at point

A(0,a)

on the positive

y

-axis, and charge

Q_3 = -2q

is at point

B(a,0)

on the positive

x

-axis. (a) Write down the expressions for the force (magnitude only) exerted on

Q_1

separately by

Q_2

and

Q_3

. (b) Resolve each of these two forces into their

x

and

y

components, taking the usual Cartesian axes. (c) Hence obtain the algebraic expressions for the net

x

and

y

components of the force acting on

Q_1

. (d) Derive an expression for the magnitude

F

and the direction (angle with the positive

x

-axis) of the net force on

Q_1

in terms of

q

a

, the constant

k = \frac{1}{4\pi\varepsilon_0}

, and elementary functions. (e) Finally, evaluate

F

numerically for

q = 2\,\mu\text{C}

and

a = 5\,\text{cm}

. Express your answer in newton correct to two significant figures.