Electric Field due to multiple point charges

[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

Homework Equations

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?

 

[gneill]

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

Homework Equations

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.

 

[tarkin]

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!