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A small ball of mass m and positive charge q is suspended by a light insulating thread from a point on a very large vertical non-conducting sheet. The sheet has a uniform positive surface charge density . In equilibrium, the thread makes an angle with the vertical. If the surface charge density of the sheet is increased to 3 , the new equilibrium angle of the thread with the vertical becomes . Which of the following

Options

  1. A= 3
  2. B= 3
  3. C= 3
  4. D= 1 3

Correct answer

C. = 3

Step-by-step solution

The electric field produced by a large vertical non-conducting sheet is uniform and horizontal, given by E = 2 _o . In the equilibrium position, the forces acting on the charged ball are the tension T in the thread, the gravitational force mg downwards, and the horizontal electric force qE . Balancing the forces in the horizontal and vertical directions: T = qE T = mg Dividing the two equations gives: = qE mg = q 2 _o mg This shows that is directly proportional to the surface charge density . When the surface charg

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