Chapter 17, Problem 1CQ

(a)

To determine

Whether the electric field do positive or negative work when the charge $-q$ moves closer to $+Q$.

Answer to Problem 1CQ

The electric field does positive work when the charge $-q$ moves closer to $+Q$.

Explanation of Solution

When we move two opposite charges close together, their initial and final kinetic energies will be zero, so the external force does negative work and the electric field does positive work.

Write the expression for the external work.

    $W_{\text{ext}}=\Delta U=-W_{\text{field}}$

Here, $W_{\text{ext}}$ is the external work done, $\Delta U$ is the change in the potential energy and $W_{\text{field}}$ is the work done on the field.

Therefore, the electric field does positive work when the charge $-q$ moves closer to $+Q$.

(b)

To determine

Whether the potential $-q$ move through a potential increase or decrease.

Answer to Problem 1CQ

The potential increases as $-q$ moves closer to $+Q$.

Explanation of Solution

The expression to find the potential is $U_E=k\frac{q_1{q}_2}{r_{12}}$. The separation distance is inversely proportional to the potential. Thus as the charge moves closer, the potential increases.

Therefore, the potential increases as $-q$ moves closer to $+Q$.

(c)

To determine

Whether the potential energy decreases or increases.

Answer to Problem 1CQ

The potential energy decreases.

Explanation of Solution

For charges of opposite signs, the potential energy decreases due to the negative sign in the potential energy term. Thus, the potential energy decreases for two opposite signs approaching each other.

(d)

To determine

When the fixed charge is changed to $-Q$, the type of work done by the electric field, the change in potential and the change in potential energy.

Answer to Problem 1CQ

The electric field does negative work, the potential decrease and the potential energy increases.

Explanation of Solution

When the charges are both negative, the electric field is doing negative work, the repulsion of the charges cause the potential to decrease and the potential energy increases.

Therefore, the electric field does negative work, the potential decrease and the potential energy increases.