14) A small charged plastic ball is vertically above another charged small ball

Question

14) A small charged plastic ball is vertically above another charged small ball in a frictionless test tube as shown in the figure. The balls are in equilibrium a distance d apart. If the charge on each ball is doubled, the equilibrium distance between the balls in the test tube would become

A),fd. B) 2d C) 4d. D) 8d. E) d4. 15) Two identical small charged spheres are a certain distance apart, and each one initially experiences an electrostatic force of magnitude F due to the other. With time, charge gradually diminishes on both spheres by leaking off. When each of the spheres has lost half its initial charge, what will be the magnitude of the electrostatic force on each one? A) 1/16 F B) 1/8 F C) 1/4 F D) 1/2 F

Explanation / Answer

14.) The electromagnetic force is given by F = (1/4o) (Q1Q2/d2  )

So, if charges are doubled reach the force will become 4 times the previous force, to bring it back to normal the distance has to double. Since denominator also will get a factor of 4 (22) if d is doubled.

So, Ans = 2d

15.) By observing the formula F = (1/4o) (Q1Q2/d2  ) we see that the force is directly proportional to the charge . So, if the new charges are Q1/2 and Q2/2 ,The force will be F' = (1/4o) ((Q1/2)(Q2/2)/d2  ) = (1/4)((1/4o) (Q1Q2/d2  )) = F/4

So, ans = 1/4 F

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