# Electric Field due to multiple point charges

## 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?

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gneill
Mentor

## 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.

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!