Direct Current Electrical Motor Model in external magnetic field Bz direction and a electric circuit with battery, brush, split rings and a rotating coil.

# Direct Current Electrical Motor Model

Electric motors turn electricity into motion by exploiting electromagnetic induction. A current-carrying loop that is placed in a magnetic field experiences a turning effect.A simple direct current (DC) motor is illustrated here. ABCD is mounted on an axle PQ. The ends of the wire are connected to a split ring commutator at position X & Y. The commutator rotates with the loop. Two carbon brushes are made to press lightly against the commutators.

The motor features a external magnet (called the stator because it’s fixed in place) and an turning coil of wire called an armature ( rotor or coil, because it rotates). The armature, carrying current provided by the battery, is an electromagnet, because a current-carrying wire generates a magnetic field; invisible magnetic field lines are circulating all around the wire of the armature.

The key to producing motion is positioning the electromagnet within the magnetic field of the permanent magnet (its field runs from its north to south poles). The armature experiences a force described by the left hand rule. This interplay of magnetic fields and moving charged particles (the electrons in the current) results in the magnetic force (depicted by the green arrows) that makes the armature spin because of the torque. Use the slider current I to see what happens when the flow of current is reversed. The checkbox current flow & electron flow alows different visualization since I = d(Q)/dt and Q= number of charge*e. The Play & Pause button allows freezing the 3D view for visualizing these forces, for checking for consistency with the left hand rule .

Description:

the following case describe a postive current i, postive B field, θ start (defined as angle between area vector of coil A and B field) = 90o , split-ring commutator gap β2= 80o

The split-ring commutator allows electricity flows from the positive terminal of the battery through the circuit, passes through a copper brush [rectangle black boxes] to the commutator, then to the armature.

Postive current runs through ABCD as shown in the diagram (select the checkbox labels?), a +y direction force would act on AB. An -y direction force would act on CD. Taking moments about the axle conveniently, reveals a resultant torque T = Fmag*AD*cosθ acts on the coil loop. The coil loop rotates in an clockwise manner (view from battery side) starting 90o until it reaches the θ = 170o position (assuming that split ring angle are default at β2 = 80o). At this θ = 170+o position, the current is cut off. However, the momentum of the loop carries it past the horizontal position until the coil loop reaches θ = 190o position. Contact between loop and split ring commutator is established again and the current in the coil loop is now reversed (note that current i is still positive). A -y direction force now acts on AB while a +y direction force acts on CD. The rotation motion is reinforced clockwise (view from battery side) as θ continues to rotate from 190o to 350o. At this θ = 350+o position, the current is cut off. However, the momentum of the loop carries it past the verticall position until the coil loop reaches θ = 10o position. Contact between loop and split ring commutator is established again and the current in the coil loop is now reversed back to same as at θ = 90o. A a +y direction force would act on AB. An -y direction force would act on CD and the loop reaches θ = 90o . The cycle repeats after θ = 90o allowing the armature to experience torque in the reinforced direction at the right time to keep it spinning.

Function of split-ring commutator:

The purpose of the commutator is to reverses the direction of the current in the loop ABCD for every half a cycle.

A swing back and fro motion (maybe θ = 90o increase to 270o and decrease back to 90o) is all you would get out of this motor if it weren't for the split-ring commutator — the circular metal device split into parts (shown here in teal with a gap of β2) that connects the armature to the circuit.

# Exercises:

The external magnetic field Bz can be varied using the slider Bz. When Bz is positive, it is in the directionof + Z axis (look at the axes of direction of the 3D view). Vary Bz until it is negative, what is the direction of the Bz then?
The current comes from the battery higher potential end and travels in a wire forming a closed circuit and travels back to the lower potential end of the battery. When θ = 90o current flows from the battery higher potential end, to the top brush, to the AB side split ring, through the coil loop in order ABCD, back to CD side split ring, bottom brush and lower potential end of the battery. What is the direction of the current flow in wire AB? What is the direction of the current flow in wire CD? using Fleming's left-hand rule, deduce the relative directions in terms of x, y and z axis notations (rather than in, up and right which is confusing) of force acting on i) AB ii) CD iii) BC iv) DA. hint: note that Fmag = I*B*L*sin(I&B) may be useful.
By taking moments about the axle PQ, consider the forces on AB and CD, deduce the direction of the torque and the motion if the coil loop was initially at rest (ω = 0 deg/s). Select the suitable sliders of your choice and verify your hypothesis for 2 angles. Discuss with your partner what you have discovered. Ask your teacher if there are any problem/issues faced using this virtual lab.
Explain and show the equations involving torque ( in earlier part of question), why the forces on wire BC and DA did not contribute to the calculation of rotating torque about axle PQ?
By considering the forces in the x direction for wire BC and DA, suggest what can happen to the coil loop if the forces are large enough. Suggest why it does not happen in terms of the properties of the wires in the coil loop.
Explain how a current-carrying coil in a magnetic field experiences a turning effect and that the effect is increased by increasing (i) the number of turns on the coil, (ii) the current (iii) increasing the magnitude of the external Bz field
After conducting some inquiry exploration on the virtual DC motor model discuss how this turning effect is used in allowing the coil loop to rotate. You may click on the show graphto reveal a scientific plot for multiple representations of the quantities versus angle and time. You may right click on the screen and select "Open EJS Model" from the pop-up menu to examine the model equations of the motion. You must, of course, have EJS installed on your computer.
Describe the action of a split-ring commutator in a two-pole magnet setup, single-coil motor. Suggest the effect adding a soft-iron cylinder in the winding the coil.
Advanced Learner:
Please submit your remix model that model features that are not available in the existing virtual lab and share your model with the world through NTNUJAVA Virtual Physics Laboratory http://www.phy.ntnu.edu.tw/ntnujava/index.php?board=28.0. Impacting the world with your model now.

### Credits:

The Direct Current Electrical Motor Model was created by Fu-Kwun Hwang (original model found here http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=912.0) , heavily customized by Loo Kang WEE (newer model found here http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1266.0) using the Easy Java Simulations (EJS) version 4.3.3.3 authoring and modeling tool. An applet version of this model is available on the NTNU website < http://www.phy.ntnu.edu.tw/ntnujava/ >.

You can examine and modify this compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: <http://www.um.es/fem/Ejs/> and in the OSP comPADRE collection <http://www.compadre.org/OSP/>.