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Chapter 21: Problem 9

A point charge is located a fixed distance outside of a uniformly charged sphere. If the sphere shrinks in size without losing any charge, what happens to the force on the point charge?

Short Answer

Expert verified
The force on the point charge remains the same since the total charge on the sphere and the center-to-point charge distance have not changed, despite the sphere shrinking in size.

Step by step solution

01

Understand the Forces

Recognize that the force between two charges is given by Coulomb's Law \( F = k \frac{q1*q2}{r^2} \). For a point charge and a uniformly charged sphere, the sphere's charge acts as if it is located at its center. The shrinking of the sphere without losing any charge does not affect its centred nature.
02

Analyze the Changes

Note that the sphere shrinks without losing any charge. The total charge on the sphere \( q2 \), and the distance between the center of the sphere and the point charge \( r \), do not change.
03

Apply Coulomb's Law

Since both \( q2 \) and \( r \) remain constant and \( r \) still measures to the center of the sphere, the force \( F \) on the point charge as per Coulomb's Law remains the same even though the sphere has shrunk.

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