A current, I=15 A, is directed along the positive x -axis...

A current, $I=15 \mathrm{A},$ is directed along the positive $x$ -axis and perpendicular to a uniform magnetic field, The conductor experiences a magnetic force per unit length of $0.12 \mathrm{N} / \mathrm{m}$ in the negative $y$ direction. Calculate the magnitude and direction of the magnetic field in the region through which the current passes.

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Key Concepts

Lorentz Force

The Lorentz force describes the force experienced by a current-carrying conductor when it is placed in a magnetic field. It is given by the cross product F = I L × B, which indicates that both the magnitude and the direction of the force depend on the current, the length of the conductor, and the magnetic field, as well as the sine of the angle between the current and the magnetic field vectors.

Magnetic Field Magnitude Calculation

When a conductor carrying a current is subjected to a known force per unit length, the magnitude of the magnetic field can be calculated by rearranging the Lorentz force formula. Specifically, when the current and the magnetic field are perpendicular, the equation simplifies to B = (F/L) / I, making it easy to determine the field’s magnitude with the given values.

Right-Hand Rule

The right-hand rule is a technique used to determine the direction of the force on a current-carrying conductor in a magnetic field. By aligning the thumb with the current, and the fingers with the magnetic field, the direction in which the palm pushes represents the force experienced by the conductor. This rule is crucial for understanding the vector nature of the magnetic force.

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