Three charges q, uniform circular motion

In summary, two positively charged spheres with a stationary negatively charged sphere between them move at a constant velocity of 12.0m/s in uniform circular motion. To find the magnitude of charge q, the equations for electric force and centripetal force can be used, but the mass of the two side spheres is needed. Assuming a mass of 1kg and later changing it to ½kg, the solution can be found and the charge will depend on the mass.
  • #1
colmes
4
0

Homework Statement



Two spheres have a charge of q a stationary sphere between them has a charge of -q. The 2 positive spheres move like conical pendulums at a constant velocity of 12.0m/s in uniform circular motion. What is the magnitude of charge q?


Homework Equations



Electric Force = kq1q2/(r^2)
(mv^2)/r = Centripetal Force
Fg = mg

The Attempt at a Solution



I did some calculations but found difficulty because I don't know that mass of the two side spheres were.
 

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  • #2
I would call them 1kg, to get a solution ; later you change them to ½kg, or "m"
(the charge will or course be different; this will get you the dependence on m)
 

What is the concept of "three charges q" in relation to uniform circular motion?

The term "three charges q" refers to a system of three point charges (q1, q2, and q3) that are arranged in a circular motion. These charges may have the same or different magnitudes, and their positions and directions of motion are carefully controlled.

How do the charges interact with each other in uniform circular motion?

In a system of three charges q, the charges interact with each other through the electromagnetic force. This force is proportional to the product of the charges and inversely proportional to the square of the distance between them. The direction of this force is always perpendicular to the line connecting the charges and follows the right-hand rule.

What is the role of centripetal force in this system?

In uniform circular motion, the centripetal force is responsible for keeping the charges in their circular path. This force acts towards the center of the circle and is equal in magnitude to the product of the mass and the square of the velocity divided by the radius of the circle.

How does the radius of the circle affect the motion of the charges?

The radius of the circle determines the strength of the centripetal force required to keep the charges in uniform circular motion. A larger radius will require a smaller centripetal force, while a smaller radius will require a larger centripetal force. This relationship is described by the equation Fc = mv^2/r.

What are some real-world applications of this concept?

The concept of "three charges q" in uniform circular motion has several real-world applications, such as in particle accelerators, where charged particles are guided in circular paths to achieve high speeds. It is also used in the design of electric motors and generators, where the circular motion of charges is harnessed to produce electrical energy.

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