Video Transcript
A long, straight wire is carrying a constant current 𝐼 that produces a magnetic
field 𝐵. Which of the following diagrams most accurately represents magnetic field lines of
𝐵? (A), (B), (C), (D), or (E).
To begin, let’s first refresh our memories about the magnetic field produced by a
long, straight, current-carrying wire and how to represent it using field lines. First, recall that a long, straight, current-carrying wire produces a magnetic field
composed of concentric closed circles. Right away then, we can eliminate answer options (C) and (E) since they do not fit
this description.
The remaining options all do show the field lines as closed concentric circles. What’s different about them though is how the circles are distributed. Recall that when we represent a magnetic field using field lines, areas where the
field lines are closer together show where the magnetic field is stronger. So, to recognize which of the remaining answer options is correct, it’ll be helpful
to recall the formula for the strength of the magnetic field 𝐵 some distance 𝑑
away from a long, straight, current-carrying wire. 𝐵 equals 𝜇 naught 𝐼 divided by two 𝜋𝑑.
Since we know that the current is constant, the only terms we need to be concerned
with here are 𝐵 and 𝑑. So, let’s write their proportionality relation. 𝐵 is proportional to one over 𝑑. We say that 𝐵 is inversely proportional to 𝑑, since as one quantity increases, the
other must decrease. This makes sense. The magnetic field is stronger closer to the wire and weaker farther away. Thus, the correct diagram will show the strength of the field decreasing with
distance from the wire.
Option (D) shows field lines that get farther apart as we look farther away from the
wire, which corresponds to the strength of the magnetic field decreasing with
distance from the wire. Therefore, (D) seems like the best choice. Diagram (A) shows equally spaced concentric circles, and diagram (B) shows the
circles getting closer together farther from the wire. Neither of these corresponds to the inversely proportional relationship between field
strength and distance from the wire. So, we can eliminate both of these options.
Thus, we know that answer choice (D) is correct. This diagram most accurately uses magnetic field lines to represent the magnetic
field surrounding a long, straight, current-carrying wire.
