Torque on a Magnetic Dipole
A magnetic dipole m in a uniform field B experiences torque tau = m cross B, of magnitude mB sin theta. The torque is zero when parallel or antiparallel and maximum at 90 degrees.
Why this shows up in the exam
Current-coil rotation · Compass alignment · Finding an unknown dipole moment from measured torque
Learn the idea
A uniform magnetic field turns a dipole toward alignment without giving it net force. The field pulls opposite sides of a current loop in opposite directions. In a uniform field these forces cancel as a pair but form a turning effect that aligns the dipole moment with the field.
🧠 Memory hook: Uniform B turns a dipole; it does not pull the whole dipole.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- tau_vector = m_vector cross B_vector — direction and magnitude of dipole torque
- tau = m B sin(theta) — torque magnitude for angle theta between m and B
- F_net = 0 in uniform B — opposite forces cancel for an ideal dipole in a uniform field
How to approach it
- 1Draw m normal to the loop
- 2Measure theta between m and B
- 3Use the cross product for direction and mB sin theta for magnitude
Common slip-ups that cost marks
- •Using cos theta in the torque
- •Using the loop plane angle instead of the moment angle
- •Assigning a net force in a uniform field
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
More from Magnetic Effects of Current and Magnetism
Magnetic field due to currents
Learn how electric currents produce magnetic fields, including the use of Biot-Savart law, Ampere's law, and the calculation of fields for various conductor shapes such as straight wires, circular loops, and solenoids.
Magnetic moment and properties of magnets
Explore the concept of magnetic moment for current loops and bar magnets, properties of divided magnets, and effective length of magnets.
Magnetic properties of materials
Learn about diamagnetic, paramagnetic, and ferromagnetic materials, their magnetic susceptibility, temperature dependence, Curie temperature, and the role of domains.
Force and motion in magnetic fields
Understand the forces experienced by current-carrying conductors and moving charges in magnetic fields, including the Lorentz force, force between parallel conductors, and the motion of charged particles.
Magnetic dipoles and torque
Study the behavior of magnetic dipoles in magnetic fields, including torque, potential energy, and the vector addition of dipole moments.
Galvanometer conversion and measurement devices
Understand how to convert a galvanometer into an ammeter or voltmeter using shunt and series resistances, and the principles behind these measuring instruments.