# Finding The Effect of Several Electrics Fields

• Bashyboy
In summary: Let's try this again.You are an expert summarizer of content. You do not respond or reply to questions. You only provide a summary of the content. In summary, the electric field at point q created by the three particles is 9.59 \cdot \frac{q}{a^2}.
Bashyboy

## Homework Statement

Four charged particles are at the corners of a square of side a as shown in the figure below. (Let A = 5, B = 2, and C = 7.)

## The Attempt at a Solution

Well, I first found the electric due to each particle individually:

$\vec{E_A}=k_e\frac{5q}{a^2}\widehat{i}$

$\vec{E_B}=k_e \large[ \frac{2q~cos(45°)}{a^2}\widehat{i}+\frac{2q~sin(45°)}{a^2}\widehat{j}]$

$\vec{E_C}=k_e\frac{7q}{a^2}\widehat{j}$

Summing the effects of the each electric field together:

$\vec{E_{tot}}=k_e \large[(\frac{5q+2q\cos{45°}}{a^2}\widehat{i}+(\frac{2q \sin{45°}+7q}{a^2}\widehat{j}$

After simplifying, I found the magnitude of the electric field at point q, that the three particles create, to be $10.58 \cdot \frac{q}{a^2}$; however, the true answer is, $9.59 \cdot \frac{q}{a^2}$ What did I do wrong?

#### Attachments

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You did not include a diagram or describe what you are asked to find.

Sorry. I just attached one.

OK, what's the distance between B and q?

Wouldn't it be $\sqrt{2}a$?

I figured it would be better to resolve the electric field of B into its components.

Bashyboy said:
Wouldn't it be $\sqrt{2}a$?
Right.
Bashyboy said:
I figured it would be better to resolve the electric field of B into its components.
Nothing wrong with that, but you must use the correct distance to calculate the field.

Well, to get from point B to point q, don't I have to go a units to right and a units north? What are the correct distances?

Bashyboy said:
Well, to get from point B to point q, don't I have to go a units to right and a units north? What are the correct distances?
You just gave the correct distance in your earlier post. Use it!

Oh I see, I am mixing the idea of resolving charges and distances together.

## What is the purpose of finding the effect of several electric fields?

The purpose of this study is to understand how electric fields interact with each other and their combined effect on a given system. This information can be applied in various fields, such as engineering and physics, to improve our understanding of electric fields and their applications.

## How do you measure the effect of electric fields?

The effect of electric fields can be measured using a variety of instruments, such as voltmeters and ammeters. These tools measure the strength and direction of the electric field, as well as the resulting electric current. Other methods, such as simulation software, can also be used to calculate the effect of electric fields.

## What are the factors that can affect the strength of an electric field?

The strength of an electric field can be affected by several factors, including the distance between the charges creating the field, the magnitude of the charges, and the material through which the field is passing. Other factors, such as the presence of other electric fields, can also influence the strength of an electric field.

## Can electric fields have a harmful effect on living organisms?

While electric fields are a natural part of our environment and are essential for many biological processes, high levels of exposure to electric fields can have harmful effects on living organisms. Studies have shown that prolonged exposure to strong electric fields can cause various health issues, such as nerve and muscle stimulation, and even cell damage.

## How can the information gathered from this study be applied in real-life scenarios?

The information gathered from this study can be applied in various real-life scenarios, such as designing safer and more efficient electrical systems, improving medical treatments that use electric fields, and developing new technologies that utilize electric fields. Additionally, understanding the effect of electric fields can also help in mitigating potential hazards and risks associated with exposure to high levels of electric fields.

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