An electric current flows into the page. What is the direction of the magnetic field?

Question

BlackTom AI · Accepted Answer

Using the right-hand rule (or right-hand grip rule): point your right-thumb in the direction of the conventional current and your curled fingers show the direction of the magnetic field lines encircling the wire.

Relevant concepts:
- A straight current-carrying wire produces concentric circular magnetic field lines around the wire.
- The right-hand rule gives the sense (clockwise or counterclockwise) of those circles for a given current direction.
- Biot–Savart law / vector cross product (dB ∝ I dl × r̂) provides a quantitative direction check.

Step-by-step reasoning (hand-rule):
1. The current is into the page (often drawn as an "×"). Point your right thumb into the page (away from you).
2. Your fingers curl around the wire; when viewed from the front of the page those fingers curl clockwise.
3. Therefore the magnetic field around the wire circles clockwise.

Vector (cross-product) check at a specific point:
1. Let the wire lie at the origin and current I be along −k (into the page). Choose a point to the right of the wire at +x (r̂ = +i).
2. Use dl × r̂: dl is along −k, so dl × r̂ = (−k) × i.
3. Compute k × i = j, so (−k) × i = −j. That is the −y direction (down) at the right-hand point, which matches clockwise circulation (top → right → bottom → left → top).
4. Similar cross products at other points produce directions consistent with clockwise loops.

Why the correct answer is correct:
- Both the intuitive right-hand grip and the cross-product calculation show the magnetic field circles clockwise when the current points into the page.

Why other options are incorrect:
- (a) Counter-clockwise is the opposite sense (would be for current out of the page).
- (b), (c), (e) (linear directions right/top/bottom) are incorrect because the field is circular around the wire, not along a single straight direction.

Conclusion: The magnetic field direction is clockwise, confirming answer d.

An electric current flows into the page. What is the direction of the magnetic field?单项选择题

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