A straight, vertical wire carries a current of 2.60 A downward in a region between the poles of a large superconducting electromagnet, where the magnetic field has magnitude B = 0.588 T and is horizontal. What are the magnitude and direction of the magnetic force on a 1.00 cm section of the wire that is in this uniform magnetic field, if the magnetic field direction is (a) east?

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Identify the given values: The current I in the wire is 2.60 A, the magnetic field B is 0.588 T, and the length of the wire segment L is 1.00 cm (which is 0.01 m). The magnetic field direction is east, as shown in the image.

Use the formula for the magnetic force on a current-carrying wire: F = I * L * B * sin(θ), where θ is the angle between the direction of the current and the direction of the magnetic field.

Determine the angle θ: Since the current is downward and the magnetic field is horizontal towards the east, the angle between them is 90 degrees. Therefore, sin(θ) = sin(90°) = 1.

Substitute the values into the formula: F = 2.60 A * 0.01 m * 0.588 T * 1.

Determine the direction of the force using the right-hand rule: Point your thumb in the direction of the current (downward) and your fingers in the direction of the magnetic field (east). Your palm will face the direction of the force, which is towards the north.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Magnetic Force on a Current-Carrying Wire

The magnetic force on a current-carrying wire in a magnetic field is given by the equation F = I * L * B * sin(θ), where I is the current, L is the length of the wire, B is the magnetic field strength, and θ is the angle between the current direction and the magnetic field. This force is perpendicular to both the wire and the magnetic field.

Right-Hand Rule

The right-hand rule is a mnemonic for determining the direction of the magnetic force on a current-carrying wire. Point your thumb in the direction of the current and your fingers in the direction of the magnetic field; the force direction is perpendicular to both, indicated by the palm. In this scenario, with the current downward and the field east, the force is directed north.

Magnetic Field

A magnetic field is a vector field surrounding magnets and electric currents, characterized by the magnetic field strength B, measured in teslas (T). It exerts a force on moving charges and current-carrying wires. In this problem, the field is uniform and horizontal, affecting the wire section within its region, influencing the force direction and magnitude.

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