Question

Which of the following statements is (are) true? a) There will be no change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed on the outer surface. b) There will be some change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed on the outer surface. c) There will be no change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed at the center of the sphere. d) There will be some change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed at the center of the sphere.

Short answer

Question: Determine the truthfulness of each statement about the change in the charge on the inner surface of a hollow conducting sphere when additional charge is either placed on the outer surface or placed at the center of the sphere: a) There will be no change in the charge on the inner surface if additional charge is placed on the outer surface. b) There will be some change in the charge on the inner surface if additional charge is placed on the outer surface. c) There will be no change in the charge on the inner surface if additional charge is placed at the center of the sphere. d) There will be some change in the charge on the inner surface if additional charge is placed at the center of the sphere. Answer: The true statements are (a) and (c).

Step-by-step solution

Understanding the basic properties of conductors

In conductors, electric charge can move freely. When a conductor reaches an electrostatic equilibrium, the following properties can be observed: 1. The electric field inside the conductor is zero. 2. The electric charges reside on the surface of the conductor. 3. The electric field just outside the conductor is perpendicular to the surface.

Analyzing statement (a)

Statement (a) states that there will be no change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed on the outer surface. Since the charges inside a conductor will redistribute on the surface when the conductor is in electrostatic equilibrium, any additional charge on the outer surface will not cause any change in the charge on the inner surface. Therefore, statement (a) is true.

Analyzing statement (b)

Statement (b) is the opposite of statement (a), so that it states there will be some change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed on the outer surface. This statement contradicts statement (a). Since statement (a) is true, statement (b) must be false.

Analyzing statement (c)

Statement (c) states that there will be no change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed at the center of the sphere. It is important to mention that putting an additional charge at the center of the hollow sphere does not violate the electrostatic equilibrium conditions. Therefore, in this case, the charges will redistribute in such a way that the net electric field inside the conductor is still zero. As a result, there will be no change in the charge on the inner surface of the sphere, which makes statement (c) true.

Analyzing statement (d)

Statement (d) is the opposite of statement (c), so that it states there will be some change in the charge on the inner surface of a hollow conducting sphere if additional charge is placed at the center of the sphere. This statement contradicts statement (c). Since statement (c) is true, statement (d) must be false. In conclusion, the true statements are (a) and (c).