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Electromagnetism

Torque on a Current Loop in a Magnetic Field

A current loop in a magnetic field experiences a turning effect that depends on the angle between its area normal and the field.

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Source & review

Difficulty

Intermediate

Read time

5 min

Prerequisites

Basic algebra, consistent units, and the stated model assumptions

Review statusNeeds review

Source

OpenStax, College Physics 2e, §22.8 (Paul Peter Urone and Roger Hinrichs)

OpenFormulaGraph equation reference; FormuLab adaptation details and license are provided below.

Adapted from OpenFormulaGraph, under CC BY 4.0.

FormuLab adapted wording, notation, applicability conditions and topic placement, and expanded the numerical check into a worked example. The textbook section reference was corrected.

Definition
Understanding the core concept

A current loop in a magnetic field experiences a turning effect that depends on the angle between its area normal and the field. The torque is greatest when those directions are perpendicular.

Variables & Units
Understanding each component
SymbolMeaningUnits
Torque
Number of coil turns
Electric current
Area enclosed by one turn
Magnetic Field
Angle
Real-World Applications
Where this formula is used in practice

Motor coils

Estimate turning effect on a current loop.

Coil orientation

Compare torque as the loop rotates in a field.

Worked Example
Step-by-step calculation with real numbers

Problem

A 50-turn coil of area 0.0100 m² carries 2.00 A in a 0.300 T field. Its area normal is perpendicular to the field. Find the torque magnitude.

Given

Solution

1
2
3

Final Answer

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