Question

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

Short answer

The net charge on the neutral conducting sphere remains zero, and the charge is distributed non-uniformly over the entire surface of the sphere due to the influence of the external point charge, so the correct answer is (C).

Step-by-step solution

Understand the behavior of a conductor in an electric field

In the presence of an external electric field, free electrons within a conductor rearrange themselves to cancel the external field within the conductor's interior. This phenomenon is known as electrostatic shielding.

Analyze the effect of the positive point charge on the conducting sphere

When the positive point charge is placed outside the conducting sphere, it induces a separation of charges within the sphere. Electrons within the conductor will move towards the side of the sphere closest to the positive charge, creating an induced negative charge on the near side.

Determine the charge distribution on the sphere's surface

The induced negative charge will be most concentrated at the point on the sphere closest to the point charge due to its attraction to the positive charge. Meanwhile, a positive charge is induced on the far side of the sphere. The charge on the surface of the sphere is therefore distributed non-uniformly.

Confirm the net charge on the conducting sphere

The net charge on the conducting sphere itself remains zero, as the induction process only redistributes the charges within the conductor; it does not add or remove charge from the sphere.

Key concepts

Electrostatic Shielding

Electrostatic shielding is a fundamental principle of electromagnetism where the charges within a conductor move in response to external electric fields to guard the interior of the conductor from the influence of external charges. Imagine the conductor as a fortress; when an external electric field approaches, the 'troops' (which are the free charges, usually electrons) move to the 'walls' (the conductor's surface) to protect the 'inhabitants' (the interior of the conductor).

This redistribution of charges within the conductor results in an electric field inside the conductor that is exactly opposite in direction to the field outside, effectively canceling it out within the conductor's interior. Therefore, delicate instruments inside the conductor are protected from external electric fields, a property utilized in applications like shielding sensitive electronics or designing Faraday cages.

Charge Induction

Charge induction occurs when a charged object is brought near a conductor. In our example, when a positive charge is close to our neutral conducting sphere, the free electrons in the sphere are attracted towards the positive charge and move to the surface closest to it, creating an induced negative charge region.

This process doesn't involve adding or losing electrons but simply moving them around within the material. It's akin to rearranging the furniture in your home rather than bringing in new pieces or throwing any out. The backside of the sphere, now lacking some of these free electrons, becomes positively charged. The result is a sphere with a non-uniform charge distribution, but its net charge remains the same, in this case, neutral.

Electric Field Effects

The electric field is a concept that quantifies the influence a charge exerts on the space around it. When an electric field is present, like from our positive point charge outside the sphere, it can apply a force on other charges around it. This is not unlike the way a magnet can influence metal objects without directly touching them.

In our conducting sphere scenario, the electric field of the external charge causes the free electrons on the sphere to redistribute themselves, for they 'feel' the presence of the field and respond to minimize its effects. The closer the charges on the sphere are to the external field source, the stronger the induced effects, leading to a higher concentration of charge on the side nearest to the point charge.

Conductors in Electric Fields

Conductors are unique in the way they interact with electric fields. Unlike insulators, conductors have free charges—usually electrons—that can move with relative ease throughout the material. When a conductor is placed in an electric field, these free charges immediately realign to counteract and neutralize the field within the conductor's body.

In our scenario, where a positive point charge is near the neutral conducting sphere, the mobile electrons in the conductor migrate towards the side of the sphere closest to the positive charge, leaving a positive charge on the opposite side. This separation of charge within the conductor under the influence of an external electric field is a vivid demonstration of the properties of conductors and how they respond to electric fields—to maintain electric neutrality internally while exhibiting induced charges on their surfaces.