Conceptual Physics

Step-by-step derivation

We use the definition of the current flowing through the wire to obtain an equation relating IL and qv. This enables us to make a substitution into the equation for the force exerted by a magnetic field on a moving charge.

We state the equation proved above as a cross product. It is the same as saying the amount of force is FB = ILB sin ș.

What is the force on the wire?

F = ILB sin ș

F = (5.0 A)(1.5 m)(0.010 T)(sin 40°)

F = 4.8×10í^2 N straight towards you

Step Reason

1. I = q/ǻt definition of current

2. IL = qL/ǻt multiply both sides by L

3. IL = qvL/ǻt equals velocity of charge carrier

4. FB = qv × B equation for force on charged particle

5. FB = IL × B substitute equation 3 into equation 4

28.19 - Physics at work: direct current electric motor

Direct current motors power a range of familiar everyday devices, from hairdryer fans to handheld electric drills. In these appliances, a few fundamental physics principles and clever engineering combine to create a motor that yields a constant amount of torque. To understand how electric motors work, recall that a magnetic field exerts a force on a wire that is conducting electricity perpendicular to the field. When the wire is in the shape of a loop, one side of the loop will experience a force in one direction, and the other in the opposite direction. This means there will be a torque on the loop and it will rotate. The magnetic moment of a coil of loops is a vector, perpendicular to each loop, used to describe how much torque the coil will experience in a magnetic field. You can think of the coil as acting like a bar magnet. When the coil’s moment is parallel to the field, it experiences no torque, since the “magnet” is lined up with the field. When it is perpendicular to the field, it experiences maximum torque. At its simplest, a direct current motor consists of a current-carrying wire coil, wrapped around a metal armature, inside a uniform magnetic field. The external field creates a torque on the coil when current flows through it. That torque is used to rotate something: a fan, a drill bit, the blades of a blender and so forth. However, a motor has two requirements that this configuration alone does not meet. First, it needs to rotate continuously in the same direction. The simple wire coil with a current will not do this: It will rotate in one direction until the field exerts no net torque on it, continue on beyond that due to its momentum, and then rotate back. The second requirement for the motor is that it should provide a nearly constant torque. The torque on a simple coil varies as the angle of the coil in the field changes. In Concept 1, you see a schematic diagram of a simplified direct current motor. Two permanent magnets form the circular outer edge of the motor. A magnetic field is directed from the north poles of these two magnets to the south poles. Inside these magnets is a wire coil, which is connected to a direct current, such as the current from a battery. This assembly is called a rotor. The problem of rotating the rotor in a constant direction is solved with a commutator. A commutator consists of two sets of contacts that supply current to the coil. During one- half of a rotation, the coil is in contact with one set and the current flows in one direction. During the other half turn, the coil is in contact with the other set and the current flows in the opposite direction. In Concept 2, you can see that the current keeps reversing direction, which alters the direction of the coil’s magnetic dipole moment. This reversal of current causes the rotor to keep experiencing a counterclockwise torque. The problem of supplying constant torque is addressed with multiple rotors as you see in Concept 3. At any moment in time, current flows through two of the rotors, which are at different angles to the permanent field. Although the torque on any one rotor varies

DC electric motor. The sparking copper commutator is visible between the rotors and the red plate at the top of the image.

Electric motor

Rotor: bar surrounded by wire coil Current flows through coil Current creates magnetic moment External field exerts torque on coil

Commutator