Calculating Electric Field in a Square of Charges

[MasterMatt]

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

Homework Equations

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

 

[cupid.callin]

remember that electric field is vector?

the E(field) due to q is canceled 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 :)

 

[MasterMatt]

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?

 

[cupid.callin]

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!

 

[rwisz]

Dear student,

Thank you for your question. To calculate the electric field at the center of the square, you can use the superposition principle, which states that the total electric field at a point is the vector sum of the individual electric fields due to each charge. In this case, since all charges have the same magnitude, the direction of the field will depend on the relative positions of the charges.

To find the direction of the field, you can choose a coordinate system that makes it easier to calculate the components of the electric field. For example, you can choose the x-axis to be along one of the sides of the square and the y-axis to be perpendicular to it. Then, you can calculate the electric field components for each charge and add them up to find the total electric field at the center of the square.

To determine the direction of each component, you can use the right-hand rule. For example, if the x-component of the electric field is positive, it means that the electric field points in the positive x-direction. If the y-component is negative, it means that the electric field points in the negative y-direction. By using this method, you can determine the direction of the electric field at the center of the square.

I hope this helps. Good luck with your calculations!