Unit 4: Magnetic Fields

Ampere’s Law

States that the magnetic field around a closed loop is proportional to the current flowing through the loop. It is a fundamental law in electromagnetism and is used to calculate the magnetic field produced by a current-carrying wire or a solenoid.

Biot–Savart law

This law describes the magnetic field generated by a steady electric current. It states that the magnetic field at any point is directly proportional to the current and the length of the conductor. It also depends on the distance between the point and the conductor. The direction of the magnetic field is perpendicular to both the current and the distance vector.

Magnetic fields

These are created by moving electric charges.

force from a magnetic field

F \= q(v x B)

Lorentz force (When a charged particle moves through a magnetic field, it experiences a force perpendicular to both the direction of motion and the magnetic field. )

F \= qE

When both magnetic and electric fields are present, the particle experiences a combined force that is the vector sum of the two individual forces.

F \= I L x B

When a wire carrying current is placed in an external magnetic field, it experiences a force.

B_perp \= B sin(theta)

If the wire is not perpendicular to the magnetic field, then only the component of the magnetic field perpendicular to the wire will cause a force.

T \= F * r * sin(theta)

When a wire is twisted, a torque is applied to it.

k \= T / theta

torsional stiffness

internal magnetic field created by a very long current-carrying wire

F \= μ₀I₁I₂L / 2πd

force between the wires

Biot-Savart Law

it states that the magnetic field at a point is proportional to the current density and the distance from the point to the current element.

Ampère's Law

The law states that the line integral of the magnetic field around a closed loop is equal to the current passing through the loop multiplied by a constant known as the permeability of free space.

Solenoid

Its function is to generate a strong magnetic field as a current flows through the wire.