AcademyMagnetic Fields and Forces
Academy
DC Motors
Level 1 - Physics topic page in Magnetic Fields and Forces.
Principle
A DC motor uses magnetic torque on a current loop to produce sustained rotation.
Notation
\(\tau\)
motor torque
\(\mathrm{N\,m}\)
\(N\)
number of coil turns
\(I\)
coil current
\(\mathrm{A}\)
\(A\)
coil area
\(\mathrm{m^{2}}\)
\(B\)
magnetic field magnitude
\(\mathrm{T}\)
\(\theta\)
angle between magnetic moment and field
\(\mathrm{rad}\)
Method
The same loop-torque equation drives the motor. A commutator reverses current every half-turn so the torque continues in the same rotational sense.
Loop torque
\[\tau=NIAB\sin\theta\]
Maximum torque
\[\tau_{\max}=NIAB\]
Mechanical power
\[P_{\mathrm{mech}}=\tau\omega\]
Electrical input
\[P_{\mathrm{elec}}=IV\]
Real motors also generate back emf as they spin, which reduces the current from its starting value.
Rules
Motor torque
\[\tau=NIAB\sin\theta\]
Maximum torque
\[\tau_{\max}=NIAB\]
Mechanical power
\[P=\tau\omega\]
Electrical power
\[P=IV\]
Examples
Question
A coil has
\[N=100\]
\[I=0.50\,\mathrm{A}\]
\[A=4.0\times10^{-3}\,\mathrm{m^2}\]
and \[B=0.20\,\mathrm{T}\]
Find maximum torque.Answer
\[\tau_{\max}=NIAB=(100)(0.50)(4.0\times10^{-3})(0.20)=4.0\times10^{-2}\,\mathrm{N\,m}\]
Checks
- More turns, current, area, or field increase ideal torque.
- Starting current can be large because back emf is initially zero.
- A motor converts electrical input power into mechanical output power plus losses.