Advanced Problem in Electrostatics

  1. 1. The problem statement, all variables and given/known data
    A ball of mass m with a charge q can rotate in a vertical plane at the end of a string of length l in a uniform electrostatic field whose lines of force are directed upwards. What horizontal velocity must be imparted to the ball in the upper position so that the tension in the string in the lower position of the ball is 15 times the weight of the ball.


    3. The attempt at a solution

    I don't get what is the meaning of the question. How can a sphere rotate on a string as its tangent? Why will tension in the string change if ball is given a velocity? When it is imparted with a velocity, does the ball rotate purely or translates too?

    Don't explain how to solve, I just need help in understanding the question.
    Perhaps a figure might help.
    Thanks
     
  2. jcsd
  3. It's hard to know what the question is asking, I think. Was a diagram included?

    Perhaps the ball is on the end of the string with the string's other end fixed in space. Then the ball would be confined to a disk around that point. Also, by "rotation," could it mean that the ball is moving in a circle around that point rather than rotating on its own axis?

    If that is the case then it would make sense that the tension on the string depends on the ball's velocity because of centrifugal force.
     
  4. Imagine you have one end of the string in your hand, at the other end is the charged sphere. Now you can slowly start swinging the sphere like a pendulum. If you go faster and faster, at some point the sphere will no longer swing back, but complete the circle. It will rotate in a vertical plane.
    Now you just have to equate gravitational, electric and centrifugal force to find the answer.

    Btw. crazy teacher who defined this problem to be electrostatics. There is not much static going on.
     
  5. Oh! I got it.
    I thought the sphere rotates about its own axis on the string.
    Thanks
     
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