3 Point Charge Coulomb's Law problem

[Kastner86]

Homework Statement

3 Point charges are fixed in place in a right triangle. What is the electric force on the +1.0 nanoC charge due to the other two charges?

Basically you have 3 charges in a right angle as decribed, let's call them A, B, and C. In the upper left you have A, +0.8 nanoC. 8cm directly below is B, -0.6 nanoC. To the right of B at unkown distance is C, +1.0 nanoC. the distance AC is given as 10 cm.

So what is the electric force on charge C?

Homework Equations

I know I need Coulomb's Law. F_E=k$$\bullet$$q1$$\bullet$$q2/d²

The Attempt at a Solution

so first i convert all charges from nanoC to C to make things easier so the charges are:

A= 8e-7
B=-6e-7
C=1e-6

then i use pathagreom's theorum to find the distance BC, which is 0.06m.

Then I draw all the Force components on point C.

First I solve for F_B using Coulomb's Law and get 1.5N in the -x direction.

This seems to fine. I get stuck when trying to get the forces between point A and C...

I can get the angles... sin^-1(0.06/0.1)= 37 degrees.

but i honestly have no clue what to do next, and have been scouring resources on the net for a solution and finally ended up here, still with no answer... please help!

 

[Kastner86]

hey thanks for everyone who looked at my question. i finally figured out the answer though! the net electric force on C should be 1.2 N at 28 degrees from the negative x axis

 

[nlightner]

Hello,

Thank you for sharing your problem with us. I would approach this problem by first drawing a diagram of the situation, labeling the charges and distances, and identifying the direction of the electric force on charge C. From the given information, we know that the electric force on charge C is due to the other two charges, A and B.

To solve for the electric force on charge C, we can use Coulomb's Law, which states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. In mathematical terms, this can be written as F = k * q1 * q2 / d^2, where k is the Coulomb's constant, q1 and q2 are the charges, and d is the distance between them.

To find the electric force on charge C, we need to consider the forces from both charges A and B. We can break down the forces into their x and y components, as the charges are not directly aligned with each other. Using trigonometry, we can find the x and y components of the force from each charge, and then add them together to get the total electric force on charge C.

The x-component of the force from charge A can be found by multiplying the magnitude of the force (calculated using Coulomb's Law) by the cosine of the angle between the line connecting charges A and C and the x-axis. Similarly, the y-component of the force from charge A can be found by multiplying the magnitude of the force by the sine of the angle. We can do the same for the force from charge B, and then add the x and y components together to get the total force on charge C.

I hope this helps you solve the problem. If you need further assistance, please don't hesitate to reach out to your teacher or a tutor for additional support. Keep up the good work in your studies!