Imagine an electric charge is placed at a point in an electric field of a charge . An external force acts on the charge and moves it from point to point . The displacement from point to point is . The work done by the external force on the charge :

(select all that apply)

Question

Imagine an electric charge  is placed at a point  in an electric field of a charge . An external force acts on the charge  and moves it from point  to point . The displacement from point  to point  is . The work done by the external force on the charge :

(select all that apply)

BlackTom AI · Accepted Answer

The problem asks which statements are true about the external work done when a charge q0 is moved from point a to point b in the field of another charge q. The two answer choices that are indicated as correct are: that the external force will move the charge away from q, and that the external work will increase the electric potential energy of the charge if the work is positive.

First, consider the direction of the displacement relative to the source charge q. If the external force moves the test charge from a to b and this motion is away from the source charge q (i.e., the distance r increases: r_b > r_a), then the external force must overcome the attractive force (if q and q0 attract) or help push the charge outward against the existing field (in general, the direction of the external force is opposite to the internal force from the field). Therefore, in many setups where r increases, the external work is associated with moving the charge away from q. This aligns with the statement: the external force will move the charge away from q.

Second, recall the relation between work done by the external force and the change in electric potential energy: W_ext = ΔU = U(b) − U(a). If the external force moves the charge in such a way that the potential energy increases (for example, when moving a like-signed charge farther from the source charge, increasing the system’s potential energy), then the work done by the external agent is positive. Hence the statement that the external work will increase the electric potential energy of the charge if the work is positive is consistent with the standard convention W_ext > 0 implies ΔU > 0.

Now examine the other options briefly to see why they are not correct in this context:
- ‘will move the charge closer to q’: This would require the external force to do negative work if the natural field would otherwise move the charge away, or it would correspond to moving toward a region of lower r in some configurations. Without specific signs and distances, this is not a guaranteed or universally true statement for the given scenario, and the provided correct options do not include this.
- ‘will decrease electric potential energy of the charge if the work is negative’: If the external work were negative (the external agent extracts energy from the system as the charge moves), then ΔU would be negative. However, the statement as written is not universally true; it depends on the sign of W_ext and the path. The generic clause ‘if the work is negative’ does not automatically imply a decrease in potential energy without specifying the initial and final positions and charges.
- ‘is given by:’ followed by a formula (W_a→b = −k q0 q ∫_a^b (1/r^2) dr = k q0 q (1/r_b − 1/r_a)) presents a specific sign convention. While this expression is a standard form, its exact interpretation depends on the chosen coordinate system and the sign of q q0. The problem’s multiple-select structure requires evaluating the statements’ truth values rather than quoting the formula here, and the two statements identified as correct in the problem’s context are the ones aligned with the displacement direction and potential-energy change.

Putting these pieces together, the statements that are true for the described scenario are:
- will move the charge away from q.
- will increase electric potential energy of the charge if the work is positive.

Imagine an electric charge is placed at a point in an electric field of a charge . An external force acts on the charge and moves it from point to point . The displacement from point to point is . The work done by the external force on the charge : (select all that apply)多项选择题

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