Question

Two charged spherical conductors, Sphere 1 and Sphere 2, are connected by a long conducting wire. A total charge q>0is placed on this combination, where Sphere 1 has a radius r₁and Sphere 2 has a radius r₂(r₂>r₁) Which of the following statements is true?

A) The charge on Sphere 1 (q1q 1​ ) is equal to the charge on Sphere 2 (2q 2​ ).
B) The electric potential of Sphere 1 is greater than the electric potential of Sphere 2.
C) The electric field at the surface of Sphere 1 is greater than the electric field at the surface of Sphere 2.
D) The total charge (q) is distributed equally on both spheres.
E) The capacitance of Sphere 1 is greater than the capacitance of Sphere 2.

Answer 1

The capacitance of Sphere 1 is greater than the capacitance of Sphere 2 because capacitance is directly proportional to radius.

Step-by-step explanation:

The correct statement is E) The capacitance of Sphere 1 is greater than the capacitance of Sphere 2.

The capacitance of a conductor is directly proportional to its radius. Therefore, because Sphere 2 has a larger radius than Sphere 1 (r₂ > r₁), Sphere 2 will have a greater capacitance. Capacitance is a measure of how much charge can be stored on an object per unit voltage, so Sphere 2 can hold more charge than Sphere 1 at the same voltage.

For example, if both spheres were connected to a battery, the voltage across both spheres would be the same. However, the larger capacitance of Sphere 2 means that it can store more charge than Sphere 1 at that same voltage.