A single-turn current loop, carrying a current of 8.00 A, is in the shape of a right triangle w

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A single-turn current loop, carrying a current of 8.00 A,...

A single-turn current loop, carrying a current of $8.00 \mathrm{~A}$, is in the shape of a right triangle with sides $50.0,120$, and $130 \mathrm{~cm}$. The loop is in a uniform magnetic field of magnitude $75.0 \mathrm{mT}$ whose direction is parallel to the current in the $130 \mathrm{~cm}$ side of the loop. What is the magnitude of the magnetic force on (a) the $130 \mathrm{~cm}$ side, (b) the $50.0 \mathrm{~cm}$ side, and (c) the $120 \mathrm{~cm}$ side? (d) What is the magnitude of the net force on the loop?

Key Concepts

Magnetic Force on Current-Carrying Conductors

This concept explains that a segment of a conductor carrying an electric current in a magnetic field experiences a force given by F = I(L × B). The magnitude of the force depends on the current (I), the length of the conductor in the field (L), the magnetic field strength (B), and the sine of the angle between the current direction and the magnetic field (?).

Cross Product and Angle Dependence

The magnetic force arises from the cross product of the length vector (representing the direction of current) and the magnetic field vector, emphasizing that the force’s magnitude is also dependent on the sine of the angle between these two directions. This means that if the current is parallel to the magnetic field, the force is zero, while it is maximized when the current is perpendicular to the field.

Uniform Magnetic Field

A uniform magnetic field has constant magnitude and direction across space, which simplifies the analysis of the magnetic forces on different segments of a current loop. In such fields, the force on each segment can be calculated independently using the same magnetic field value.

Net Force on a Closed Current Loop

For a closed loop in a uniform magnetic field, even though individual segments may experience nonzero forces, the overall net force on the loop can be zero because the forces on opposite sides of the loop can cancel out. This concept is crucial to understanding the equilibrium and motion of current loops in magnetic fields.

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