Electric Point Forces in a Circle

In summary, the problem involves twelve identical point charges equally spaced around a circle of radius R, with one charge being moved to the center of the circle. The magnitude of the net electric force on this charge can be found using the principle of superposition, by first calculating the force as if there were still 12 charges and then subtracting the force of the one charge outside the circle. The direction of the net electric force can be expressed as an integer.
  • #1
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Homework Statement


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.

Homework Equations

The Attempt at a Solution


PART A:
- i drew the diagram of a circle with radius R and one of the 12 points at the center.
- i am fairly certain i need to use the principle of superposition but with 11 other points I am not sure where to start

PART B:
- didnt attempt yet because need part A first.

Any help at all would be appreciated I am so confused!
 
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  • #2
hi toosha88! :smile:

hmm :rolleyes: … with 11 equations to deal with, i'd be looking for a short-cut :biggrin:

hint: try calculating the force as if there were still 12 charges round the circle …

then calculate the difference with only 11 :wink:
 
  • #3
Thanks for the advice! But, if i were to calculate the force in the middle of the circle wouldn't that just equal zero?
Would i then just calculate the force on the ONE charge inside the circle?
Im still confused!:confused:
 
  • #4
hi toosha88! :smile:

(just got up :zzz: …)
toosha88 said:
Thanks for the advice! But, if i were to calculate the force in the middle of the circle wouldn't that just equal zero?

Yup! :biggrin:
Would i then just calculate the force on the ONE charge inside the circle?

(i assume you mean from the one charge outside the circle?)

yes, but you'd need to subtract it, wouldn't you? :wink:
 
  • #5


I would first like to clarify that the term "electric point forces" is not a commonly used term in physics. It would be more accurate to refer to this situation as "electric point charges in a circle".

Now, let's address the problem at hand. You are correct in thinking that the principle of superposition will be useful in solving this problem. This principle states that the net force on a point charge due to a group of other point charges is equal to the vector sum of the individual forces exerted by each charge.

PART A:
To find the magnitude of the net electric force on the charge at the center, we will need to calculate the individual forces exerted by each of the other 11 charges. Since all the charges are identical, we can simply calculate the force exerted by one charge and multiply it by 11. The magnitude of the force between two point charges q1 and q2, separated by a distance r, is given by Coulomb's law:

F = k * (q1*q2)/r^2

Where k is the Coulomb constant (8.99x10^9 N*m^2/C^2). In this case, q1 and q2 are the charges of the two point charges and r is the distance between them. Since all the charges are the same, we can rewrite this equation as:

F = k * (q^2)/r^2

Now, we need to find the distance between the charge at the center and each of the other 11 charges. Since they are equally spaced around the circumference of the circle, the distance between any two adjacent charges will be 2πR/12. Therefore, the distance between the charge at the center and each of the other 11 charges is R.

Plugging in the values, we get:

F = k * (q^2)/R^2

Since we have 11 other charges, the net force on the charge at the center will be:

Fnet = 11 * k * (q^2)/R^2

PART B:
To find the direction of the net electric force, we need to consider the direction of each individual force. Since the charges are all the same, the direction of each force will be either towards or away from the center. If we look at the diagram, we can see that the forces exerted by the charges on the left side of the circle will be towards
 

1. What is an electric point force in a circle?

An electric point force in a circle is a type of force that acts on a charged particle moving in a circular path. This force is perpendicular to the direction of motion and is caused by the presence of an electric field.

2. How does an electric point force affect the motion of a charged particle?

An electric point force causes a charged particle to accelerate towards the center of the circle, changing the direction of its motion. This results in the particle moving in a circular path.

3. What is the relationship between the strength of the electric point force and the radius of the circle?

The strength of the electric point force is directly proportional to the radius of the circle. This means that as the radius increases, so does the strength of the force. Similarly, as the radius decreases, the force also decreases.

4. How does the magnitude of the charge of the particle affect the electric point force in a circle?

The magnitude of the charge of the particle has a direct impact on the strength of the electric point force. A higher magnitude of charge will result in a stronger force, while a lower magnitude will result in a weaker force.

5. Can an electric point force in a circle be calculated?

Yes, an electric point force in a circle can be calculated using the formula F=qvB, where F is the force, q is the charge of the particle, v is the velocity of the particle, and B is the strength of the magnetic field. This formula can be used to determine the magnitude and direction of the force acting on a charged particle in a circular path.

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