# Solving Electric Field Equations: A Case Study

• SteelDirigibl
In summary, The student is having trouble with an equation for solving electric fields and forces. They have attempted to use the equation E=ke*q/r2 but are unsure of where they have gone wrong in their calculations. The correct equation should be F=q*E and there is a mistake with the value of √2.

E=ke*q/r2

## The Attempt at a Solution

See screenshot. The angles are correct, however I can't get the equation right for either part. I understand they should be different since one is force and the other electric field, I thought that should be the electric field solved and simplified.

Not sure how to put in equations on here, so I'll do my best.
before simplification, I had for the i component:
ke3q/a2+sqrt(2)/2*ke4q/a2

and for the j component:
ke5q/a2+sqrt(2)/2*ke4q/a2

where have I gone wrong? the sqrt(2)/2 is cos(45) and sin(45) to get the components of the Bq in the drawing. Not sure what the problem is. I can do these fine with numbers so maybe I just am not putting it into the computer right. suggestions?

Ei = ke3q/a²+sqrt(2)/2*ke4q/a² = kq/a²[3 + 2√2]
In the screenshot, you have √2 when you should have 2√2.
Same in the j part.

Use F = q*E to get the force - same expression, just square the q.

## What are electric field equations?

Electric field equations are mathematical equations that describe the behavior of electric fields, which are regions of space where electrically charged particles experience a force. These equations help us understand and predict the behavior of electric fields in various situations.

## Why is it important to solve electric field equations?

Solving electric field equations allows us to understand and predict the behavior of electric fields, which is crucial in many applications such as electronics, power generation, and telecommunications. It also helps us design and optimize systems that use electric fields, making them more efficient and effective.

## What is a case study in the context of solving electric field equations?

A case study in the context of solving electric field equations refers to a specific example or scenario where these equations are applied to solve a problem or analyze a system. It allows us to see how these equations work in a real-world situation and understand their practical implications.

## What are some common techniques for solving electric field equations?

Common techniques for solving electric field equations include using integral and differential calculus, applying the principle of superposition, and using numerical methods such as finite element analysis. These techniques can be used alone or in combination, depending on the complexity of the problem.

## Are there any limitations to solving electric field equations?

While electric field equations are powerful tools for understanding and predicting the behavior of electric fields, they have some limitations. They may not be accurate in certain extreme or non-uniform situations, and they do not take into account quantum effects. Additionally, the complexity of the equations may make it challenging to solve them for certain systems.