Question

a positive charge moves in the direction of an electric field. which of the following statements are true? check all that apply. the electric field does negative work on the charge. the electric field does positive work on the charge. the electric field does not do any work on the charge. the potential energy associated with the charge increases. the amount of work done on the charge cannot be determined without additional information. the potential energy associated with the charge decreases.

Explanation:

Step1: Recall work - energy relation in electric field

The work done by an electric field on a charge is related to the change in its potential energy. The work - energy theorem for an electric field is $W =-\Delta U$, where $W$ is the work done by the electric field on the charge and $\Delta U$ is the change in the potential energy of the charge.

Step2: Analyze work done by electric field

When a positive charge moves in the direction of an electric field, the electric field does positive work on the charge. Mathematically, if the force on the positive charge due to the electric field is $\vec{F}=q\vec{E}$ (where $q> 0$) and the displacement $\vec{d}$ is in the direction of $\vec{E}$, then $W = Fd\cos\theta$ with $\theta = 0^{\circ}$ (so $\cos\theta=1$) and $W>0$.

Step3: Analyze change in potential energy

Since $W =-\Delta U$ and $W>0$ for a positive charge moving in the direction of the electric field, $\Delta U<0$. This means the potential energy associated with the charge decreases.

Answer:

The electric field does positive work on the charge. The potential energy associated with the charge decreases.