Find the electric field at the point P on a right triangle

[ino]

Homework Statement

https://www.physicsforums.com/threads/find-the-electric-field-in-the-point-p-of-a-right-triangle.965285/#post-6125768 knowing that the three charges are equal and that the angles of the triangle are 90°, 45°, 45°.

Homework Equations

The Attempt at a Solution

I tried solving it by calculating the total force on each charge, decomposing it

on the X and Y axis and calculating then the total force acting on P. But I'm not sure if it is correct:

 

[berkeman]

Welcome to the PF.

First, if the charges Q1, Q2 and Q3 are all the same, and the point P is equidistant between Q1 and Q3, what can you say about the net electric field at P due to those two charges?

Second, the problem is asking for the E-field at P, not the net force. Can you write the simplified equation for the E-field at point P now that you've thought about the net field from Q1 and Q3?

 

[haruspex]

I am mystified by your working. You seem to be calculating forces between the three charges. These have nothing to do with the question asked.

 

[ino]

Welcome to the PF.

First, if the charges Q1, Q2 and Q3 are all the same, and the point P is equidistant between Q1 and Q3, what can you say about the net electric field at P due to those two charges?

Second, the problem is asking for the E-field at P, not the net force. Can you write the simplified equation for the E-field at point P now that you've thought about the net field from Q1 and Q3?

The net field due to Q1 and Q3 is 0; so the electric field will be E = k Q2 / r^2, where r is the distance between Q2 and P.
Is it correct?

 

[haruspex]

The net field due to Q1 and Q3 is 0; so the electric field will be E = k Q2 / r^2, where r is the distance between Q2 and P.
Is it correct?

Right.

 

[berkeman]

so the electric field will be E = k Q2 / r^2, where r is the distance between Q2 and P.

Correct. Now all you have left to do is express r in terms of the given distance d.