Torque on a Current Loop in a Magnetic Field
Investigates the torque experienced by a current-carrying loop placed in a uniform magnetic field and introduces the concept of magnetic dipole moment.
What is Torque on a Current Loop in a Magnetic Field?
A twisting or turning force that tends to cause rotation.
Key formula / rule: Torque on a Current Loop
Key points
- To derive the expression for the torque on a current-carrying loop in a uniform magnetic field.
- To define and calculate the magnetic dipole moment of a current loop.
- To understand the factors affecting the torque on a current loop.
- To relate the torque on a current loop to its potential energy in a magnetic field.
Common exam trap
Confusing the angle φ (between normal to the loop and B) with the angle between the plane of the loop and B.
Definitions
- Term
Torque
- Meaning
A twisting or turning force that tends to cause rotation.
- Term
Magnetic Dipole Moment
- Meaning
A measure of the magnetic strength and orientation of a magnetic source, such as a current loop or a bar magnet. For a current loop, it is defined as the product of the current, the area of the loop, and the number of turns.
Learning objectives
To derive the expression for the torque on a current-carrying loop in a uniform magnetic field.
To define and calculate the magnetic dipole moment of a current loop.
To understand the factors affecting the torque on a current loop.
To relate the torque on a current loop to its potential energy in a magnetic field.
Formulae
- Name
Torque on a Current Loop
- Note
N = number of turns, I = current, A = area of loop, B = magnetic field strength, \φ = angle between the normal to the plane of the loop and the magnetic field.
- Expression
\τ = NIAB \sin(\φ)
- Name
Magnetic Dipole Moment
- Note
m is the magnitude of the magnetic dipole moment. The direction of m is perpendicular to the plane of the loop, given by the right-hand rule.
- Expression
m = NIA
- Name
Torque in terms of Magnetic Dipole Moment
- Note
Vector form: \vec{\τ} = \vec{m} \× \vec{B}
- Expression
\τ = mB \sin(\φ)
- Name
Potential Energy of a Magnetic Dipole
- Note
Vector form: U = -\vec{m} \· \vec{B}
- Expression
U = -mB \cos(\φ)
Prerequisites
Understanding of magnetic fields.
Knowledge of Lorentz force on a current-carrying wire (F = ILB sin(θ)).
Basic concepts of torque and rotational motion.
Vector cross product.
Common mistakes
Confusing the angle φ (between normal to the loop and B) with the angle between the plane of the loop and B.
Forgetting to include the number of turns (N) in calculations.
Incorrectly applying the right-hand rule for the direction of torque or magnetic moment.
Assuming the torque is always maximum or zero without considering the orientation.
Keywords
Torque
Current Loop
Magnetic Field
Magnetic Dipole Moment
Uniform Magnetic Field
NIAB sin(φ)
Electric Motor
Galvanometer
Potential Energy
Practice preview
A circular coil of radius r carrying current I is placed in a uniform magnetic field B. The magnetic dipole moment of the coil is M. What is the magnitude of the torque acting on the coil when its plane is perpendicular …
easy
A current loop of area A is placed in a uniform magnetic field B. The magnetic dipole moment of the loop is M. Which of the following statements is correct regarding the torque on the loop?…
medium
A current loop of magnetic dipole moment M is in unstable equilibrium in a uniform magnetic field B. What is the potential energy of the loop?…
medium