Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net

Q: Why doesn't the positive charge pull electrons completely out of the sphere?

The electric force from the point charge is usually not strong enough to overcome the work function of the metal, which is the energy required to completely remove an electron from the material's surface. The electrons just move to the boundary.

Q: If the near side is negative, isn't the sphere negatively charged?

No, because the far side becomes equally positively charged. The *local* charge density changes, but the *global* net charge remains exactly zero.

Q: What would happen if we touched the sphere while the positive charge was nearby?

If you touch it (grounding it), electrons from the ground would flow into the sphere, attracted by the positive point charge. Then, if you remove your finger, the sphere *would* have a net negative charge! But in this problem, the sphere is isolated.

Q: Are the induced charges uniformly distributed?

No. The negative charges will be highly concentrated on the side closest to the positive point charge, while the positive charges will be spread out on the farther side.

Q: Does the neutral sphere exert a force on the point charge?

Yes! Because the induced negative charges are closer to the point charge than the induced positive charges, the attractive force is stronger than the repulsive force. The overall neutral sphere will attract the point charge.

Question

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then

Options:

(A) negative and distributed uniformly over the surface of the sphere

(B) negative and appears only at the point on the sphere closest to the point charge

(C) negative and distributed non-uniformly over the entire surface of the sphere

(D) zero

Sigma Percentile · Accepted Answer

### The Illusion of Charge: Understanding Electrostatic Induction

Imagine you are looking at a perfectly neutral metal sphere. Suddenly, a positive point charge is brought near it. If you were to measure the electric field near the surface of the sphere, you would find that one side behaves as if it's negatively charged, while the other side acts positively charged. Does this mean the sphere has magically acquired a net charge? Let's dive into the fascinating world of electrostatic induction to find out.

### The Sea of Electrons

To understand what happens, we must first look inside the conducting sphere. A conductor, like a metal, is characterized by its "sea of free electrons." These are electrons that are not tightly bound to any specific atom and are free to roam throughout the entire volume of the material.

When a positive point charge $+Q$ is placed nearby, it generates an electric field that permeates the space around it, including the interior of the conducting sphere. The free electrons within the sphere immediately experience an attractive electrostatic force pulling them towards the external positive charge.

### Charge Redistribution (Induction)

Because they are free to move, these electrons rush towards the side of the sphere closest to the positive charge. This accumulation of electrons creates a region of **negative induced charge** on the near surface.

However, these electrons had to come from somewhere! As they migrate towards the near side, they leave behind positively charged metal ions on the far side of the sphere. This creates a region of **positive induced charge** on the surface farthest from the point charge. This entire process of charge separation without any physical contact is known as **electrostatic induction**.

### The Law of Conservation of Charge

Here is the critical catch: the sphere is completely isolated. It is not connected to the ground, nor is it touching the point charge or any other object.

According to the fundamental **Law of Conservation of Charge**, charge can neither be created nor destroyed in an isolated system. Because the sphere is isolated, no electrons have actually entered the sphere from the outside, and no electrons have left it. The total number of electrons and protons within the sphere remains exactly the same as it was before the point charge was introduced.

Therefore, if we sum up the negative induced charge on one side and the positive induced charge on the other, they must perfectly cancel each other out:

$$Q_{	ext{net}} = q_{	ext{negative}} + q_{	ext{positive}} = 0$$

The net charge on the sphere remains absolutely **zero**. Induction merely redistributes the existing charge; it does not alter the total net charge of an isolated body.

Animated Solution for Physics - Electrostatics: Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then

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Visualized Solution

$Initial Setup$

$Electrostatic Induction$

$Charge Redistribution$

$Conservation of Charge$

$Conclusion$

The Sigma Insight: Conductors

The Illusion of Charge

The Sea of Electrons

Charge Redistribution (Induction)

The Law of Conservation of Charge

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