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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 even as the sphere shrinks in size without losing any charge.

Step by step solution

01

Comprehend the problem

We consider a point charge located a fixed distance outside a uniformly charged sphere. The sphere is shrinking but keeping its total electric charge constant. We need to understand how this change in the sphere's size affects the force that the sphere's electric field exerts on the point charge.
02

Apply Coulomb's Law

Coulomb's law gives the force between two charges, such as the point charge and the charged sphere we're considering. The formula is \(F=k * |q1*q2|/r^2\), where F is the force, q1 and q2 are the charges, r is the distance between the charges, and k is Coulomb's constant. Since the point charge and the charge of the sphere remain constant, and the distance from the point charge to the sphere's center stays the same as the sphere shrinks, it implies that the force will not change.
03

Consider the electric field from a spherically symmetric charge distribution

Outside the sphere, the sphere's charge can be thought of as being concentrated at the sphere's center, so the electric field strength and therefore the force on the point charge does not depend on the sphere's radius. Inside the sphere, the electric field strength does depend on the sphere's radius. However, since the point charge is always outside the sphere as the sphere shrinks, we are only interested in the sphere's electric field outside the sphere, which does not depend on the sphere's radius. Therefore, even as the sphere shrinks, the force on the point charge stays the same.

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Most popular questions from this chapter

The charge density within a charged sphere of radius \(R\) is given by \(\rho=\rho_{0}-a r^{2},\) where \(\rho_{0}\) and \(a\) are constants and \(r\) is the distance from the center. Find an expression for \(a\) such that the electric field outside the sphere is zero.

What surface charge density on an infinite sheet will produce a 1.4-kN/C electric field?

An electron close to a large, flat sheet of charge is repelled from the sheet with a 1.8-pN force. Find the surface charge density on the sheet.

Can electric field lines ever cross? Why or why not?

A spherical shell \(30 \mathrm{cm}\) in diameter carries \(85 \mu \mathrm{C}\) distributed uniformly over its surface. A 1.0 - \(\mu\) C point charge is located at the shell's center. Find the electric field strength (a) \(5.0 \mathrm{cm}\) from the center and (b) \(45 \mathrm{cm}\) from the center. (c) How would your answers change if the charge on the shell were doubled?
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