28.6:
Magnetic Force
Consider two wires connected to a battery.
If the currents' directions are opposite, the wires repel. If the directions are the same, the wires attract.
When a test charge is placed nearby, it experiences no force, since the wires are electrically neutral. So, the force acting between the wires is not electric; this is known as the magnetic force.
If a magnetic compass is placed near the wire, the needle experiences a force and is aligned tangentially to a circle around it. As a result, concentric loops of magnetic fields are formed around the wire.
If the thumb points in the current's direction, the wrapped fingers provide the direction of the magnetic field.
For a wire with a current in the upward direction, the magnetic field points inward into the plane, and the magnetic force points to the left.
This combination of directions satisfies the right-hand rule. The magnetic force on a test charge Q moving with velocity v in a magnetic field B is Q multiplied by the cross-product of v and B, called the Lorentz force.
28.6:
Magnetic Force
In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a moving charge or a group of moving charges known as the electric current. A magnetic force is experienced by a second current or moving charge in response to this magnetic field. Fundamentally, interactions between moving electrons in the atoms of two bodies produce magnetic forces between them.
The magnetic force acting on a moving charge has four main properties. First, its magnitude is proportional to the magnitude of the charge. Secondly, the magnitude of the force is proportional to the magnitude of the field. For two identical bar magnets instead of one, the force on a moving charge particle doubles without changing its velocity and charge.
The third characteristic is that the magnetic force depends on the test charge's velocity, unlike the electric force, which remains constant whether the charge is moving or not. No magnetic force is exerted on a charged particle at rest. Fourth, the magnetic force is always perpendicular to the velocity and the magnetic field.
The magnetic force, F, on a charge, Q, moving with velocity, v, in a magnetic field, B, is
This is known as the Lorentz force law.
If the charge, Q, moves by an amount
then the work done is
Combining the three equations leads to
Hence the magnetic force does zero work. It can only change a test charge's direction of motion. The speed of the particle remains unaffected by the magnetic force.
Suggested Reading
- Griffiths, D.J. (2013). Introduction to Electrodynamics. 1900 E. Lake Ave., Glenview, IL: Pearson; section 5.1; page 210–215.
- Young, H.D. and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson; section 27.1 and 27.2; pages 885–886.