A straight wire carries an electric current upwards, to the top of the page. The current is within a uniform magnetic field directed out of the page. What is the direction of the magnetic force on the current?

Question

BlackTom AI · Accepted Answer

Use the right-hand rule for the magnetic force on a current-carrying wire: F = I(L × B). Here the current (L) points upward (toward the top of the page) and the magnetic field (B) points out of the page (represented by dots).

1. Relevant concepts
- Magnetic force on a straight wire: F = I L × B, where L is a vector along the current and B is the magnetic field vector.
- The cross product L × B gives a vector perpendicular to both L and B; the right-hand rule (or standard vector cross-product identities) sets its direction.

2. Step-by-step reasoning
- Choose a coordinate system: x to the right, y up, z out of the page. Then L (current) = (0, L, 0) along +y and B = (0, 0, B) along +z.
- Compute the cross product L × B to find the direction of F.

3. Intermediate calculation
Use the determinant formula:
L × B = det | i   j   k |
               | 0   L   0 |
               | 0   0   B |

= i*(L*B - 0) - j*(0*B - 0*0) + k*(0*0 - L*0)
= (L B) i + 0 j + 0 k
= (L B, 0, 0).

Thus L × B points along +x, i.e., to the right. Multiplying by I and the magnitude just scales the vector; the direction is unchanged.

4. Why the correct answer is correct
The force is perpendicular to both current and magnetic field and, by the right-hand rule (thumb up for current, fingers pointing out of page), the palm pushes to the right. The vector algebra confirms +x direction.

5. Why other options are incorrect
- a. To the left: opposite of the computed direction.
- c/d. To the bottom/top: those are ±y directions; force is not along the current direction.
- e. Out of the page: that is the B direction; force must be perpendicular to B and to the current, not along B.

6. Conclusion
Therefore the magnetic force on the current is to the right, confirming choice b.

A straight wire carries an electric current upwards, to the top of the page. The current is within a uniform magnetic field directed out of the page. What is the direction of the magnetic force on the current?单项选择题

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