A straight wire carries an electric current to the right. The current is within a uniform magnetic field directed into the page. What is the direction of the Lorentz force?

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First, restate the scenario: a straight wire carries current to the right, and the magnetic field is uniform and directed into the page. We want the direction of the Lorentz force on the wire.

To analyze, use the magnetic force on a current-carrying wire: F = I (L × B), where L is a vector in the direction of the current (to the right) and B is the magnetic field (into the page).

Option-by-option analysis:
- a. Out of the page: This would require L × B to point outward from the page. With L to the right and B into the page, the cross product L × B does not point out of the page, so this is not correct.
- b. To the top of the page: Compute L × B explicitly. Let L point to the right (positive x) and B point into the page (negative z). Using the cross product: x × (-z) = - (x × z) = - ( -y ) = +y, which points upward on the page. Therefore, this matches the actual direction of the force. This option is consistent with the vector calculation.
- c. Left: A force to the left would correspond to a negative y or a different cross-product result, which does not align with the computed x × (-z) direction, so this is incorrect.
- d. Right: A force to the right would be in the same direction as L, which would require a different cross product outcome. The actual cross product yields an upward force, not horizontal to the right, so this is incorrect.
- e. To the bottom of the page: This would correspond to a negative y direction, opposite the computed +y result. Since the cross product yields +y (upward), this option is incorrect.

In summary, calculating the cross product of the current direction (right) with the magnetic field (into the page) gives a force that points upward on the page, confirming option b as the correct direction.

MUF0122 Physics Unit 2 - Semester 2, 2025 9.10 Lorentz force

A straight wire carries an electric current to the right. The current is within a uniform magnetic field directed into the page. What is the direction of the Lorentz force?

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