About This Simulation: The Homopolar Motor

A homopolar motor is one of the simplest electric motors — just a battery, a strong magnet, and a piece of copper wire. Conventional current flows from the battery's positive (top) terminal, down both arms of the wire, into the conductive neodymium magnet, and back to the negative terminal. Near the side of the magnet, the magnetic field B points largely radially outward (when North is up). Each current-carrying arm therefore experiences a magnetic force F = (I × B) L that is tangential — the same way around on both arms — producing a continuous torque that spins the wire. It is called homopolar because the current always passes through the field in the same direction relative to one pole, so no commutator or switching is needed.

Concepts Illustrated

• Force on a current-carrying conductor: F = (I × B) L, where I and B are vectors and L is the scalar length of wire in the field; magnitude F = BIL sinθ.
• Fleming's left-hand rule (F-B-I): thumb = Force, first finger = Field, second finger = Current — verify each magenta arrow in the 3D view.
• Magnetic field of a magnet: field lines leave the North pole and return to the South pole; field strength decreases with distance.
• Torque and rotational equilibrium: the motor speeds up until frictional torque balances magnetic torque, reaching a steady angular speed.
• Reversing motion: reversing the current or the field reverses the spin; reversing both leaves the spin unchanged.

Check Your Understanding

1. With North facing up and conventional current flowing down the wire arms, in which direction does the wire spin when viewed from the top? Use Fleming's left-hand rule to justify your answer.
   Answer

   Clockwise (viewed from above). Near the magnet, B points radially outward and I is downward, so F = (I × B) L is tangential, driving a clockwise rotation.
2. Predict what happens to the direction of rotation if you press Reverse Current only. What if you press Reverse Current and Flip Magnet together?
   Answer

   Reversing the current alone reverses the spin (anticlockwise). Reversing both the current and the field flips the sign twice, so the spin stays clockwise.
3. Doubling the current doubles the steady spinning rate in this model. Explain why, using F = BIL and the balance between magnetic torque and friction.
   Answer

   Force on each arm is proportional to I (F = BIL), so magnetic torque doubles. Steady state occurs when frictional torque (proportional to ω) balances it, so the steady ω also doubles.
4. Set the current to 0 A. Why does the wire keep spinning for a while before stopping?
   Answer

   With no current there is no driving torque, but the wire has rotational inertia. Friction provides a small opposing torque, so the angular speed decays gradually to zero rather than stopping instantly.
5. Why doesn't a homopolar motor need a commutator (split-ring), unlike a conventional DC motor?
   Answer

   In a DC motor coil, the force on each side would reverse every half turn, so a commutator reverses the current to keep the torque one-way. In a homopolar motor the geometry is symmetric about the spin axis: the current always crosses the field the same way at every angle, so the torque never reverses and no commutator is needed.