Question

You stand at location A, a distance d from the origin, and hold a small charged ball. You find that the electric force on the ball is 0.079 N. You move to location B, a distance 2d from the origin, and find the electric force on the ball to be 0.00988 N. What object located at the origin might be the source of the field? (Select all that apply.)

a-a point charge
b-a uniformly charged hollow sphere
c-none of the above

Answer 1

An object located at the origin producing the electric field experienced by the charged ball could be either a point charge or a uniformly charged hollow sphere, as both produce an electric field that diminishes with the square of the distance, which is consistent with the force measurements provided.

Step-by-step explanation:

The object located at the origin could be a point charge or a uniformly charged hollow sphere. The electric force experienced by a charged ball at a certain distance from the origin depends on the nature of the electric field produced by the source charge.

For both a point charge and a hollow sphere, the electric field (and thus the force on a test charge) diminishes with the square of the distance from the source. In the scenario provided, we observe that when the distance is doubled (from location A to location B), the force is reduced by a factor that is consistent with an inverse square law relation (0.079 N to 0.00988 N, which is roughly a reduction by a factor of 8). Since both a point charge and a hollow sphere create an electric field that follows an inverse square law, either could be the source of the field.

We should note that this only applies outside the hollow sphere; inside, the electric field due to a uniformly charged hollow sphere is zero. But since there is no information suggesting the test charges were inside a sphere, both options remain possible sources of the field.