Question

the net electric force acting on each of the three objects below is sketched as a green arrow. for example, if the green arrow points to the left the object feels a net electric force pushing it to the left. if there is no green arrow, the object feels no net electric force. use this information to assign an electric charge to each object. that is, decide whether each object has a positive electric charge, a negative electric charge, or is neutral. note for advanced students: there may be more than one correct answer.

Explanation:

To solve this, we analyze the electric forces:

Step 1: Analyze the middle and right objects

The middle object (\(+\)) and right object (\(-\)) have a green arrow between them pointing toward the \(-\) (since opposite charges attract, the force on \(+\) is toward \(-\), and on \(-\) is toward \(+\); but the arrow between them is green, so we focus on the left object first).

Step 2: Analyze the left object

The left object has a green arrow pointing left. Let’s denote the left object as \(X\), middle as \(+\), right as \(-\).

• The middle \(+\) charge exerts a repulsive force on \(X\) (if \(X\) is \(+\)) or attractive (if \(X\) is \(-\)).
• The right \(-\) charge exerts an attractive force on \(X\) (if \(X\) is \(+\)) or repulsive (if \(X\) is \(-\)).

The net force on \(X\) is left. Let’s test:

• If \(X\) is \(-\): Repulsive force from \(-\) (right) and attractive force from \(+\) (right) → net force right (contradicts left arrow).
• If \(X\) is \(+\): Repulsive force from \(+\) (left) and attractive force from \(-\) (right). For net force left, repulsive force (left) must be stronger than attractive (right). This is possible.
• If \(X\) is neutral: A neutral object experiences induced forces, but the net force direction here (left) aligns with repulsion from \(+\) (if \(X\) were neutral, the \(+\) would induce a slight negative charge on \(X\)’s right, positive on left—so \(+\) repels the left (positive) induced charge, and \(-\) attracts the right (negative) induced charge. But the net force here is left, so the repulsive force from \(+\) dominates. However, the problem allows multiple answers, but the most straightforward is:

• Left object: \(\boldsymbol{+}\) (since repulsion from \(+\) (left) and attraction to \(-\) (right) gives net left force if \(+\)’s repulsion is stronger).
• Middle: \(+\) (given).
• Right: \(-\) (given).

Answer:

Left object: \(+\), Middle object: \(+\), Right object: \(-\) (or left could be neutral, but \(+\) is more consistent with the force direction).