Magnetic Fields
A magnetic field is a physical field caused by moving electric charges that influence electric charges, electric currents, and magnetic materials. Every atom has a magnetic field, as the electrons orbiting the nucleus are moving electric charges, although incredibly small. Every magnetic field has two poles, a north and a south. The polarity of the magnet is found only with another magnet. The magnets work similarly to Coloumbs law, where opposites attract and likes repel with a force decreasing in magnitude as distance increases.
The earth has a magnetic field because of its molten iron core. In the outer core, the molten iron holds electric currents which create the massive magnetic field that we feel. Compasses have a lightweight magnetic arrow inside them, which is attracted to the northern pole of the Earth’s magnetic field.
When a charged particle moves through a magnetic field, it experiences a magnetic force perpendicular to the magnetic field and the direction of motion. The force can be found with this equation:
F = q (v x B)
where F is the magnetic force, q is the charge, and v x B is the cross product of the particle’s velocity and the magnetic field. In this case, the cross-product would create a vector perpendicular to the particle’s velocity vector and the direction of the magnetic field. Despite interacting with it, the magnetic field does not do any work on the particle, as the force will always be perpendicular to the magnetic field, which creates 0 work.
Since no work is being done, the speed of the particle will never change, only its direction. The motion that the particle follows is called cyclotron motion. The radius and direction of the cyclotron motion depend on the particle’s velocity, charge, and mass, as well as the strength of the magnetic field.
When a current flows through a wire, a magnetic field is produced. This field interacts with other magnets, which can cause the wire to move. The force this wire feels is dependent on the length of the wire, the current flowing through the wire, and the magnetic field strength. Once again, this force will be perpendicular to the magnetic field and the current. This force is used in many generators and motors to move a coil or wire and as a sensor for magnetic fields.
In a long wire, a circular magnetic field is created that is known as a solenoid. The magnetic field of a solenoid can be calculated using Ampere’s Law:
B = μ₀ (I / 2πr)
where B is the magnetic field, I is the current, r is the distance from the wire, and μ₀ is a constant called the permeability of free space, equal to 4π times 10⁻⁷. The magnetic field is in the direction of the current in this case.
The Biot-Savart Law states that the magnetic field of a wire will be proportionate to the length of the wire and the current that runs through it. It is also dependent on a concept called the vector potential, which is a concept that defines the behavior of vector fields. In this case, the vector potential would depend on the distance from the wire and the direction of the magnetic field.
Both Ampere’s Law and the Biot-Savart Law are integral to calculating magnetic fields, and they can even be used in circuits and motors.