# 4 Charges around a square. Find the magnitude and direction of the field at thecenter

## Homework Statement

A square with sides d has charges q, 2q, 3q and 4q arranged
clockwise around the corners of the square. What are the
magnitude and direction of the field at the centre of the square?

Hints: consider pairs on opposite sides of the square. Choose a
coordinate system that makes finding components easy

E=F/q=kq/r^2

## The Attempt at a Solution

I have drawn a diagram, and I believe that I need to just calculate E for each charge, however I don't know how to approach it. Since now sign (-ve/+ve) is given for any particles how do I determine the direction of the electric field. Thanks in advance

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remember that electric field is vector?

the E(field) due to q is cancelled by E due to one of q from 3q and also of 2q due to 2q from 4q.

So you have 2 equal E's perpendicular to each other.
now, E = KQ/r2

therefore Enet = sqrt(2) x E

find r from d

also if q is at top left corner, E is downwards!!!

happy to help :)

I'm sorry, but I'm still confused. Why do Eq and E2q cancel? Also how do you get from E = KQ/r2 to Enet = sqrt(2) x E?

As the q charge and and 3q are opposite ... their E are opposite so net E because of these two charges is:

E' = (3Kq/r2) - (Kq/r2) = 2Kq/r2

same can be done for charges 2q and 4q.

E'' = (4Kq/r2) - (2Kq/r2) = 2Kq/r2

Now E' and E'' are perpendicular (remember that diagonals of square are perpendicular to each other)

So you can find Enet !!!!

and yes sorry, as charges are positive ... Enet will be upward!!!

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