A 20.0 cm ×30.0 cm rectangular loop of wire carries 1.0 A of current clockwise around the loop.

step 1 In this question, we have a loop, which is in the rectangular shape carrying a current of one am

A 20.0 cm ×30.0 cm rectangular loop of wire carries 1.0 A of...

A $20.0 \mathrm{cm} \times 30.0 \mathrm{cm}$ rectangular loop of wire carries $1.0 \mathrm{A}$ of current clockwise around the loop. (a) Find the magnetic force on each side of the loop if the magnetic field is $2.5 \mathrm{T}$ out of the page. (b) What is the net magnetic force on the loop?

A $20.0 \mathrm{cm} \times 30.0 \mathrm{cm}$ rectangular loop of wire carries $1.0 \mathrm{A}$ of current clockwise around the loop.
(a) Find the magnetic force on each side of the loop if the magnetic field is $2.5 \mathrm{T}$ out of the page.
(b) What is the net magnetic force on the loop?

Key Concepts

Magnetic Force on a Current-Carrying Conductor

This concept refers to the force experienced by a segment of wire carrying an electric current when it is placed in an external magnetic field. The magnitude and direction of the force are given by the equation F = I (L × B), where I is the current, L is the length vector of the wire segment, and B is the magnetic field. This principle is fundamental in understanding how magnetic fields interact with moving charges in conductors, which is essential for the operation of many electromagnetic devices.

Right-Hand Rule and Cross Product

The right-hand rule is a mnemonic for determining the direction of the magnetic force on a current-carrying conductor in a magnetic field, as dictated by the cross product in the equation F = I (L × B). When using the right-hand rule, point the fingers in the direction of the current (or the length vector) and curl them toward the magnetic field; the thumb then points in the direction of the force. This concept is crucial for visualizing and predicting the behavior of currents in magnetic fields.

Net Force on a Closed Current Loop in a Uniform Magnetic Field

In a uniform magnetic field, although individual segments of a closed current loop experience forces due to the magnetic field, these forces often cancel out when the entire loop is considered. This cancellation happens because the forces on opposite sides of the loop are equal in magnitude but opposite in direction, resulting in a net force of zero. Understanding this concept is important for analyzing the motion and equilibrium of current-carrying loops in magnetic fields.

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