A test charge +q and a test charge -q are released midway...

A test charge $+q$ and a test charge $-q$ are released midway between the two plates. Let the voltage of the top plate be $V$ and the voltage of the bottom plate be 0 . The distance between the two plates is $d$. Which of the following statements about the test charges are true? i. Both charges have gained a kinetic energy of $|q| E d / 2$ when they hit the plates. ii. Charge $+q$ is initially at a positive voltage and charge $-q$ is initially at a negative voltage. iii. Charge $+q$ initially has a positive potential energy and charge $-q$ initially has a negative potential energy. iv. Both charges lose potential energy. (A) i only (B) i and ii (C) i and iii (D) iii and iv (E) i, iii and iv

A test charge $+q$ and a test charge $-q$ are released midway between the two plates. Let the voltage of the top plate be $V$ and the voltage of the bottom plate be 0 . The distance between the two plates is $d$. Which of the following statements about the test charges are true?
i. Both charges have gained a kinetic energy of $|q| E d / 2$ when they hit the plates.
ii. Charge $+q$ is initially at a positive voltage and charge $-q$ is initially at a negative voltage.
iii. Charge $+q$ initially has a positive potential energy and charge $-q$ initially has a negative potential energy.
iv. Both charges lose potential energy.
(A) i only
(B) i and ii
(C) i and iii
(D) iii and iv
(E) i, iii and iv

Key Concepts

Electric Field in Uniform Regions

In problems involving parallel plates, the electric field is often assumed to be uniform. The field strength is given by the voltage difference divided by the separation between the plates (E = V/d). This concept underpins the forces experienced by test charges placed within the field and is essential for analyzing the motion and energy changes of the charges.

Electric Potential and Potential Energy

Electric potential represents the work done per unit charge to move a test charge from a reference point to a specific point in space, and it relates to potential energy by U = qV. This relationship is fundamental in understanding how the energy of a charge depends on both the magnitude and sign of the charge as well as the local voltage.

Work-Energy Conversion in Electric Fields

As charges move within an electric field, the potential energy they initially possess is converted into kinetic energy (or vice versa). The work done by the electric field coincides with the change in the charge's potential energy, a key concept in analyzing energy gains or losses during motion in electrostatic scenarios.

Behavior of Charges in Electric Fields

The motion of charges in an electric field is influenced by the sign of the charge. Positive charges naturally move from regions of higher potential to lower potential, while negative charges move from regions of lower potential to higher potential. This behavior affects how potential and kinetic energy change as charges move in the field.

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