Point charges are placed at the four corners of a square of side lying in the -plane…

PHYSICS · Subjective · AP · Physics C: Electricity and Magnetism · Electric Charges Fields and Gauss's Law · Electric Charges Fields and Gauss's Law

Problem

Point charges are placed at the four corners of a square

ABCD

of side

10\,\text{cm}

lying in the

xy

-plane with sides parallel to the axes. Let the centre of the square be the origin

O

. The charges are assigned as follows (taken in order

A \to B \to C \to D

clockwise):

+8\,\mu\text{C}

A( -5\,\text{cm},\,+5\,\text{cm})

-5\,\mu\text{C}

B(+5\,\text{cm},\,+5\,\text{cm})

+8\,\mu\text{C}

C(+5\,\text{cm},\,-5\,\text{cm})

, and

-5\,\mu\text{C}

D(-5\,\text{cm},\,-5\,\text{cm})

. (a) Determine the

x

-component and the

y

-component of the net electric field at the centre

O

. (b) Hence obtain the magnitude of the net electric field at

O

and the angle it makes with the positive

x

-axis. (c) All four charges are now doubled in magnitude while their positions remain unchanged. Without repeating the entire calculation, state how the magnitude of the net electric field at

O

will change and give a brief justification.

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