Electric Field due to Multiple Point Charges

[grandprix]

Homework Statement

Two point charges are placed on the x axis. The first charge, q1 = 8.00 nC, is placed a distance 16.0 m from the origin along the positive x axis; the second charge, q2 = 6.00 nC, is placed a distance 9.00 m from the origin along the negative x axis.

Calculate the electric field at point A, located at coordinates (0 m, 12.0 m).

Homework Equations

E=kq/r²

Calculate the distance from each charge to point A

Determine the directions of the electric fields


Calculate the components of E


Give the x and y components of the electric field as an ordered pair. Express your answer in Newtons per coulomb to three significant figures.

The Attempt at a Solution

I am not sure what to do.. I am getting confused with the components.. Can someone show m how to do this?

 

[rl.bhat]

Show your attempt. The components of E are Ecosθ and Εsinθ.

 

[tomcue]

To calculate the electric field at point A, we need to consider the contributions from both point charges. The electric field due to a point charge is given by the equation E = kq/r^2, where k is the Coulomb's constant (8.99x10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge to the point of interest.

In this case, we have two point charges, q1 = 8.00 nC and q2 = 6.00 nC, located at distances of 16.0 m and 9.00 m from the origin, respectively. To calculate the electric field at point A, we need to determine the distance from each charge to point A and then calculate the electric field contributions from each charge separately.

Distance from q1 to point A:
r1 = √(x1^2 + y1^2) = √(0^2 + 12.0^2) = 12.0 m

Distance from q2 to point A:
r2 = √(x2^2 + y2^2) = √(0^2 + 12.0^2) = 12.0 m

Now, we can calculate the electric field contributions from each charge using the equation E = kq/r^2:

Electric field due to q1:
E1 = (8.99x10^9 Nm^2/C^2)(8.00x10^-9 C)/(12.0 m)^2 = 5.99x10^-3 N/C

Electric field due to q2:
E2 = (8.99x10^9 Nm^2/C^2)(6.00x10^-9 C)/(12.0 m)^2 = 4.49x10^-3 N/C

To determine the direction of each electric field, we can use the fact that like charges repel and opposite charges attract. Since both charges are positive, the electric field from q1 will point away from it, while the electric field from q2 will point towards it.

Now, we can calculate the x and y components of the electric field at point A by using the equation E = Ecosθ (for the x component) and E = Esinθ (for the y component), where θ is the angle between the electric