Calculating Electric Field at 4th Corner of Rectangle with 3 Charges

[Pseudo Statistic]

I have this question:

Positive charges are situated at 3 corners of a rectangle with charges q1, q2, and q3. Given each of their distances from the 4th corner of the rectangle, what is the electric field at the 4th corner?

Would it be the vector sum of the electric field of each of those at the 4th corner?
So, for q1, say it's r meters away, the field at that point would be:
E = q1/(4pi epsilon0 times r^2) ...
And then, knowing the angle at which it's pointed (relative to, say, the horizontal) I'd multiply it by the cosine of that angle and sine to end up with the x and y components, rinse and repeat for all of the others, add them all up (considering directions and signs) and then use Pythagoras' theorem, then finding the direction? Or am I thinking wrong?
Just want to know if I'm thinking of the right idea!
Thanks!

 

[Chi Meson]

You are thinking correct. Do you think it couldn't possibly be so easy? Well it is.

 

[quicknote]

Yes, you are on the right track! To calculate the electric field at the 4th corner of the rectangle, you would need to use the vector sum of the electric fields produced by each of the three charges at that point. This is because electric fields are vectors and have both magnitude and direction.

As you mentioned, you would first calculate the electric field produced by each charge using the equation E = q/(4πε0r^2), where q is the charge and r is the distance from the charge to the 4th corner. Then, you would need to consider the direction of each electric field and use vector addition to find the total electric field at the 4th corner.

To do this, you would use the cosine and sine functions to find the x and y components of each electric field, and then add them together to find the total electric field in both the x and y directions. Finally, you can use the Pythagorean theorem to find the magnitude of the total electric field and the inverse tangent function to find the direction.

Remember to pay attention to the signs of the electric fields, as they can either add or cancel out depending on their direction. Keep in mind that the direction of the electric field is always pointing away from positive charges and towards negative charges.

I hope this helps clarify your thinking and approach to solving this problem. Good luck!