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

Q: Why does the sphere attract the point charge if its net charge is zero?

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.

Q: What if the sphere was an insulator?

In an insulator, electrons cannot move freely, so there would be no macroscopic charge separation, only microscopic polarization. The net charge would still be zero.

Q: How can we give the sphere a net charge using this setup?

By grounding the sphere while the positive charge is nearby, electrons from the ground would flow into the sphere. If you then remove the ground connection, the sphere would have a net negative charge.

Q: Does the electric field inside the sphere change?

No, the electric field inside a conductor in electrostatic equilibrium is always zero. The induced charges arrange themselves precisely to cancel the external field inside the conductor.

Q: Is the induced charge uniformly distributed?

No, the induced negative charge is concentrated on the side facing the point charge, while the positive charge is spread out on the opposite side.

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 presented with a perfectly neutral conducting sphere. It sits there, completely uncharged, minding its own business. Suddenly, a positive point charge is brought close to it. What happens to the sphere? Does it magically acquire a charge? This classic problem tests our fundamental understanding of electrostatic induction and the conservation of charge.

### The Microscopic Dance of Electrons

To understand what happens, we need to zoom in and look at the microscopic structure of the conducting sphere. Because it is a conductor, it contains a vast sea of free electrons that can move around easily. When the positive point charge is brought near, it creates an electric field that permeates the sphere.

These free electrons, being negatively charged, feel a strong attractive force towards the positive point charge. They migrate towards the side of the sphere closest to the point charge, creating a localized region of negative charge.

Consequently, the side of the sphere farthest from the point charge experiences a deficit of electrons, leaving behind a localized region of positive charge. This separation of charges within a neutral object due to an external electric field is known as **electrostatic induction**.

### The Law of Conservation of Charge

Now, here is the crucial part where many students make a silly mistake. It is tempting to think that because the sphere now has regions of positive and negative charge, it has somehow become charged.

However, we must remember the **Law of Conservation of Charge**. This fundamental principle states that in an isolated system, the total amount of charge remains constant.

Did we connect the sphere to the ground? No. Did we touch it with another charged object? No. The sphere is completely isolated. Therefore, no electrons could have entered or left the sphere. The charges merely rearranged themselves. The total number of protons and electrons within the sphere remains exactly the same as before.

### The Final Verdict

Since the total amount of positive charge inside the sphere is still perfectly balanced by the total amount of negative charge, the **net charge** on the sphere remains exactly **zero**.

The sphere is polarized, meaning it has a dipole moment, but its overall net charge is zero. Therefore, the correct answer is that the net charge on the sphere is zero.

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

Select Answer:

Visualized Solution

$Q_{initial} = 0$

$Electrostatic Induction$

$Q_{net} = 0$

The Sigma Insight: Conductors

The Illusion of Charge

The Microscopic Dance of Electrons

The Law of Conservation of Charge

The Final Verdict

Similar Questions