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

a) Placing additional charge on the outer surface of the sphere will not change the charge on the inner surface. b) Placing additional charge on the outer surface of the sphere will change the charge on the inner surface. c) Placing additional charge at the center of the sphere will not change the charge on the inner surface. d) Placing additional charge at the center of the sphere will change the charge on the inner surface. Answer: a) and c)

Step-by-step solution

Statement a: Additional outer charge and no change in the inner surface charge

If additional charge is placed on the outer surface of a hollow conducting sphere, the charges will redistribute on the outer surface to maintain a zero electric field inside the sphere. The inner surface remains at zero electric field, so there is no change in the charge on the inner surface. Therefore, statement a is true.

Statement b: Additional outer charge and change in the inner surface charge

This statement is the opposite of statement a. Since we have already concluded 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, statement b is false.

Statement c: Additional central charge and no change in the inner surface charge

If additional charge is placed at the center of a hollow conducting sphere, the electric field inside the sphere will be nonzero. To maintain a zero electric field in the conductor, the charges on the inner surface of the sphere will redistribute to cancel the field created by the central charge. This redistribution causes no change in the total charge on the inner surface, so statement c is true.

Statement d: Additional central charge and change in the inner surface charge

This statement is the opposite of statement c. Since we have already concluded 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, statement d is false. Therefore, the true statements are a) and c).