Twelve identical point charges are equally spaced around the circumference of a circle of radius 'R'. The circle is centered at the origin. One of the twelve charges, which happens to be on the positive axis, is now moved to the center of the circle.

Part A
Find the magnitude of the net electric force exerted on this charge.
Express your answer in terms of some or all of the variables q, R, and appropriate constants.

Part B
Find the direction of the net electric force exerted on this charge.
Express your answer as an integer. (in degrees counterclockwise from the positive x axis).

i hv the same question i understand part b but i am getting wrong answer for part a, what was the equation you used crystal?

This is a rather simple problem.

Do it with symettry.

First, find the E at the center if the all 12 charges are symettrical about the circle (wont it be zero?).

Next, then consider what if you put a charge at one position which is opposite, making a net charge of zero at that position.

Add then E from this added "virtual" charge. E=k(-q)/R^2 the negative sign means it is in the opposite direction as the original E.

Net E=kq/r^2, the E points toward the replaced charge

E=kq/r^2 doesn't seem to be the correct answer for Part A.. help?

Ofcourse, for part B, 0 degrees makes sense and is correct as you have explained.

Never mind, got it!

Thanks!!

To solve this problem, we can break it down into two parts: finding the magnitude of the net electric force and finding its direction.

Part A: Magnitude of the net electric force exerted on the charge

1. Consider the 12 identical charges arranged on the circumference of the circle. We can calculate the electric force exerted by each charge using Coulomb's law:

F = k * |q1| * |q2| / r^2

Where F is the electric force, k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them.

2. Since all 12 charges are identical and equally spaced, the force between any two adjacent charges would have the same magnitude and direction. The angle between adjacent charges on the circumference of the circle would be 360 degrees / 12 = 30 degrees.

3. To find the net electric force exerted on the charge at the center, we need to consider the vector sum of the forces. Since all the forces are acting in the same direction (the positive x-axis) and have the same magnitude, we can simply multiply the magnitude of the force between each adjacent charge by 11 (as there are 11 adjacent charges) to get the net force.

Net Force = 11 * F

Where F is the electric force calculated in step 1.

Part B: Direction of the net electric force exerted on the charge

4. Since all the forces are acting in the same direction (the positive x-axis), the net force will also be acting in the same direction.

5. Therefore, the direction of the net electric force exerted on the charge can be represented as an angle counterclockwise from the positive x-axis. In this case, the angle would be 0 degrees.

To summarize:

Part A: The magnitude of the net electric force exerted on the charge is 11 times the magnitude of the electric force between any two adjacent charges.

Part B: The direction of the net electric force exerted on the charge is 0 degrees counterclockwise from the positive x-axis.