# Electric Field due to multiple point charges

• tarkin
In summary, the electric field at point P is E1x + E2y, where x and y are the magnitude and direction of the components, respectively.
tarkin

## Homework Statement

[/B]
Derive expressions for the magnitude and direction of the electric field at point P and the potential
at R.

Charges Q1 and Q2 are both positive.

Distance from Q1 to P is h, distance from Q2 to P is √2 h

E = k q/r^2

## The Attempt at a Solution

I started with finding E field at point P for each of the 2 charges, giving:

E1 = k Q1/h^2

E2 = k Q2/2h^2

Then separate into x and y components.
For E1, the x component is 0, and the y component is just the total E1.
For E2, the x component is E2 * cos45 , and the y component is E2 * sin45. (I think.)

Is it okay to give the answer as just (magnitude) x direction + (magnitude) y direction ?

Or should the answer be given as just 1 number for magnitude, and one angle for direction? Wouldn't this give some horrible expression?

tarkin said:

## Homework Statement

[/B]
Derive expressions for the magnitude and direction of the electric field at point P and the potential
at R.

Charges Q1 and Q2 are both positive.View attachment 112977

Distance from Q1 to P is h, distance from Q2 to P is √2 h

E = k q/r^2

## The Attempt at a Solution

I started with finding E field at point P for each of the 2 charges, giving:

E1 = k Q1/h^2

E2 = k Q2/2h^2

Then separate into x and y components.
For E1, the x component is 0, and the y component is just the total E1.
For E2, the x component is E2 * cos45 , and the y component is E2 * sin45. (I think.)
You should sketch in the vectors on the figure so that you can get an idea of the directions of the components. No doubt there's angles of 45° involved, but a sketch will help you to locate where those angles sit.
Is it okay to give the answer as just (magnitude) x direction + (magnitude) y direction ?

Or should the answer be given as just 1 number for magnitude, and one angle for direction? Wouldn't this give some horrible expression?
If the question doesn't specify a preferred method then either format for a vector should be acceptable. You might find that the expression for the angle simplifies a good amount through cancellation of variables.

gneill said:
You should sketch in the vectors on the figure so that you can get an idea of the directions of the components. No doubt there's angles of 45° involved, but a sketch will help you to locate where those angles sit.

If the question doesn't specify a preferred method then either format for a vector should be acceptable. You might find that the expression for the angle simplifies a good amount through cancellation of variables.

Okay, thank you!

## 1. What is the formula for calculating the electric field due to multiple point charges?

The formula for calculating the electric field due to multiple point charges is given by:E = k * Q / r^2, where E is the electric field, k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), Q is the charge of the point charge, and r is the distance between the point charge and the point where the electric field is being calculated.

## 2. Can the electric field due to multiple point charges be negative?

Yes, the electric field due to multiple point charges can be negative. The sign of the electric field depends on the direction of the force that the electric field exerts on a positive test charge. If the force is in the opposite direction of the electric field, then the electric field will be negative.

## 3. How does the electric field due to multiple point charges change if the distance between the charges is increased?

If the distance between the charges is increased, the electric field due to multiple point charges will decrease. This is because the electric field follows an inverse square law, meaning that the strength of the electric field decreases as the distance between the charges increases.

## 4. What is the net electric field due to multiple point charges?

The net electric field due to multiple point charges is the vector sum of the individual electric fields due to each point charge. This means that you must add up the magnitudes of the individual electric fields and take into account their direction to find the net electric field at a specific point.

## 5. Can the electric field due to multiple point charges be affected by the presence of other charges?

Yes, the electric field due to multiple point charges can be affected by the presence of other charges. This is because charges can interact with each other and their electric fields can combine or cancel out at certain points. It is important to take into account the presence of all charges in a given system when calculating the electric field due to multiple point charges.

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