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:

Step1: Analyze the leftmost object

The leftmost object has a net force to the left. Let's consider the middle object's force (to the left) and the rightmost object's force (to the left on the middle, so by Newton's third law, middle exerts right on rightmost? Wait, no, let's use charge interactions: like charges repel, opposite attract. Let's denote the left object as A, middle as B, right as C.

Force on A: left. So what's causing it? Let's see B's force on A. If B is, say, negative, and A is positive, B would attract A (force on A to the right), but A's force is left. Wait, maybe A is negative, and B is negative? No, repel. Wait, maybe A is neutral? No, neutral has no net force from charged objects? Wait, no, the problem says to assign charge (positive, negative, neutral) based on net force.

Wait, let's re-examine the arrows:

- Left object (A): green arrow left → net force left.

- Middle object (B): green arrow right → net force right.

- Right object (C): green arrow left → net force left.

Now, let's think about charge interactions:

- If two charges are same (both + or both -), they repel (force on each is away from each other).

- If two charges are opposite, they attract (force on each is towards each other).

Let's assume:

- Let's start with B. B has net force right. So the force from A on B and force from C on B. Let's say A and C:

Suppose C is negative. Then if B is positive, C (negative) attracts B (positive) → force on B to the right (towards C). Then A: if A is negative, A (negative) repels B (positive)? No, opposite attract. Wait, A (negative) and B (positive) would attract → force on B to the left (towards A). But B's net force is right, so force from C (right) must be stronger than force from A (left). So B: force from C (right) > force from A (left).

Now A: net force left. Force from B (positive) on A (negative) is attraction → force on A to the right (towards B). But A's net force is left, so there must be another force? Wait, no, only three objects: A, B, C. So A interacts with B, B interacts with A and C, C interacts with B.

Wait, maybe A is neutral? No, neutral has no net force from charged objects? Wait, no, the problem allows neutral, but if A is neutral, the force on A would be zero (no green arrow), but A has a green arrow left. So A must be charged.

Alternative approach: Let's assign charges step by step.

1. Left object (A): force left. So the force on A is from B. If B is positive, and A is negative, B attracts A → force on A to the right (towards B) → no, that's right. If B is negative, and A is negative, they repel → force on A to the left (away from B) → that works! So A: negative, B: negative? But then B's force from A: repel (force on B to the right, away from A) and force from C: let's see C.

2. Middle object (B): force right. So force from A (negative) on B (negative) is repel → force on B to the right (away from A). Then force from C: if C is positive, B (negative) and C (positive) attract → force on B to the right (towards C) → so total force on B is right (from A repel and C attract). Then C: force left. Force from B (negative) on C (positive) is attract → force on C to the left (towards B). That works!

So let's check:

- A: negative (force from B (negative) repel → left).

- B: negative (force from A (negative) repel → right; force from C (positive) attract → right → net right).

- C: positive (force from B (negative) attract → left).

Yes, that works.

Alternatively, other combinations:

- A: positive, B: positive, C: negative.

Check:

- A (positive) force from B (positive) repel → left (good, A's force is left).

- B (positive) force from A (positive) repel → right; force from C (negative) attract → right (good, B's force is right).

- C (negative) force from B (positive) attract → left (good, C's force is left).

Yes, that also works.

So possible assignments:

Case 1:

- A: negative (⊖), B: negative (⊖), C: positive (⊕)

Case 2:

- A: positive (⊕), B: positive (⊕), C: negative (⊖)

Let's verify Case 2:

- A (⊕) and B (⊕): repel → force on A is left (away from B) → correct (A's arrow left).

- B (⊕) and A (⊕): repel → force on B is right (away from A); B (⊕) and C (⊖): attract → force on B is right (towards C) → net right (correct, B's arrow right).

- C (⊖) and B (⊕): attract → force on C is left (towards B) → correct (C's arrow left).

Yes, that works.

So either:

- Left: ⊕, Middle: ⊕, Right: ⊖

or

- Left: ⊖, Middle: ⊖, Right: ⊕

Let's choose one, say the second case for clarity.

Step2: Assign charges

- Left object (A): negative (because force is left, repelled by middle negative).

- Middle object (B): negative (repels left object, attracts right positive).

- Right object (C): positive (attracted by middle negative, force left).

Answer:

Left object: negative (⊖), Middle object: negative (⊖), Right object: positive (⊕)
(or Left: positive, Middle: positive, Right: negative, both are correct)