Problem 145 - Master Resource Book in JEE Main Physics

Question

Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then [IIT JEE 2007] (a) negative and distributed uniformly over the surface of sphere (b) negative and appears only at the point on the sphere closed to the point charge (c) negative and distributed non-uniformly over the entire surface of the sphere (d) zero

Step-by-Step Solution

Answer

(d) zero; the sphere's net charge remains zero.

Step 1: Understand Influence of External Charge

When a positive point charge is placed near a neutral conducting sphere, it induces a separation of charges on the sphere. The electrons in the sphere's material will be attracted toward the side closer to the positive charge, creating an induced negative charge on that side.

Step 2: Analyze Charge Distribution on the Sphere

Since the sphere is a conductor, free electrons within it can move easily. The positive charge influence causes electrons to accumulate more on the part of the sphere that is closer to the charge, resulting in a non-uniform distribution of negative charge.

Step 3: Consider the Net Charge of the Sphere

Despite the induced negative charge on the side of the sphere nearest to the positive charge, the sphere as a whole remains electrically neutral. The positive charge induced on the far side balances the negative charge induced near the point charge, meaning the net charge of the sphere is zero.

Step 4: Identify Correct Option

From the above analysis, the sphere remains overall neutral (net charge zero) as it started with no excess charge, and induction only rearranges existing charges without adding or removing them. Therefore, the correct option is (d) zero.

Key Concepts

Induced charge

Induced charge occurs when a charged object is brought near a conductor. This charged object does not touch the conductor, but it still influences the movement of the conductor's electrons. When this happens, charges within the conductor redistribute themselves. For example, if a positive charge is near a conducting sphere, it attracts electrons from the sphere's surface toward it. This movement of electrons leaves an induced negative charge on the surface nearest to the point charge. The side further from the point charge becomes positively charged due to the deficit of electrons. This separation of charge occurs solely because of the proximity of the charged object. It's important to understand that in this process, the conductor itself doesn’t gain or lose any total charge; it merely rearranges its charges.

Conductor charge distribution

In conductors, free charges move easily in response to electric fields. When an external charge is placed near a conducting sphere, the distribution of its internal charges changes. The side of the sphere facing the external positive charge becomes negatively charged as electrons congregate there. The opposite side of the sphere, now lacking some of its electrons, becomes positively charged. This creates a non-uniform charge distribution, with an excess of negative charge on the side nearest the external positive charge and a relative positive charge on the far side.

• The proximity of the external charge determines how concentrated the charges will be on different areas of the sphere.
• Conductors have electrons that are free to move, which facilitates this redistribution of charge.

However, even with this non-uniform distribution, the total charge of the sphere remains zero as it started with no excess charge.

Neutral conducting sphere

A neutral conducting sphere initially has no net charge. It means that the number of positive charges, often protons fixed within atoms, equals the number of electrons that move freely across the sphere. When a charged object, such as a positive point charge, is brought near the sphere, the sphere undergoes charge redistribution. The key point here is that while the distribution of charges changes, the total or net charge of the sphere remains zero.

• Electrons move, but no new electrons or positive charges are added or removed from the sphere.
• Its overall neutrality is preserved, though its surface charge distribution becomes altered.

This ability to remain neutral while still affecting how charges are arranged is a significant property of conductors.

Charge induction effect

The charge induction effect is an electrostatic phenomenon where a charged object causes a redistribution of charge within a nearby conductor. This does not involve any physical contact between the charged object and the conductor. Instead, the presence of the charge creates an electric field that influences the conductor's free electrons, causing them to move. For instance, if a conductor is initially neutral and a positive charge is brought near, electrons within the conductor are attracted toward the positive charge, causing the near side to have an excess of negative charge.

• Induction can cause a conductor to demonstrate apparent polarity, where one part shows an excess negative charge while another shows a positive charge.
• Such effects are temporary and last only as long as the external charge is present.

Once the external influence is removed, the charges within the conductor will return to their uniform distribution, effectively neutralizing the charge differences that the induction effect caused.