Electric Field due to multiple point charges

AI Thread Summary
To derive the electric field at point P due to two positive charges Q1 and Q2, the electric field contributions E1 and E2 are calculated using the formula E = k q/r^2. The components of E1 are solely in the y-direction, while E2 has both x and y components influenced by a 45° angle. A sketch is recommended to visualize the vector directions and angles involved. The discussion highlights that either a component format or a single magnitude and angle format for the answer is acceptable, depending on the problem's specifications. Simplification of the angle expression may occur through variable cancellation.
tarkin
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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.
pointcharges.jpg


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?
 
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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

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.
 
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!
 
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