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While fiddling about in the electronics lab, you manage to charge a solid ball o

ID: 1407003 • Letter: W

Question

While fiddling about in the electronics lab, you manage to charge a solid ball of insulating material so that there is a tight concentration of charge at the center which decreases quadratically to 0 at the boundary of the ball in a spherically symmetric manner. You want to compare the total charge of this ball to the total charge it would have if the charge density was uniform. In other words, what's the ratio of the total charge of the non-uniform case versus the uniform case. Assume that the two cases have the same charge density at the center of the ball.

Explanation / Answer

Total charge enclosed is density times total volume

In a case, same amount of charge density ( either uniform charge distibution or non-uniform charge distribution), the total chage inside the sphere in uniform and total charge in non-uniform case is same.Thus, the ratio of the total charge of the non-uniform case versus the uniform case is 1:1.