We have a hollow metallic sphere with charge −5.9 µC and radius 5 cm.We insert a +10-µC charge at the center of the sphere through a hole in the surface.What charge now rests on the outer surface of the sphere?

Question

We have a hollow metallic sphere with charge −5.9 µC and radius 5 cm.We insert a +10-µC charge at the center of the sphere through a hole in the surface.What charge now rests on the outer surface of the sphere?
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Quizplus · Accepted Answer

Due to the conductive property of the sphere, charges will move freely within it and distribute themselves uniformly on the surface. Thus, initially, the -5.9 µC charge is uniformly distributed on the entire surface of the sphere.

When we insert a +10 µC charge at the center of the sphere, the negative charge on the surface of the sphere is attracted toward the center of the sphere, while the positive charge on the surface is repelled outward. This redistributes the charges on the surface until a new equilibrium is reached.

To find the final charge on the surface of the sphere, we can use the fact that the net charge inside the sphere remains the same both before and after the insertion of the +10 µC charge. Initially, the net charge inside the sphere is -5.9 µC. After the +10 µC charge is inserted, the net charge inside the sphere becomes +4.1 µC (10 µC - 5.9 µC).

Therefore, the charge on the outer surface of the sphere must be equal in magnitude but opposite in sign to the net charge inside the sphere, giving us a final charge of +4.1 µC on the outer surface.

Hence, the best choice is A) +4.1 µC.

We Have a Hollow Metallic Sphere with Charge −5