# Electric current, electric charge, magnetic field, magnetic force

In 1819, a Danish scientist named Hans Christian Oersted (1777-1851) discovered the relationship between magnetism and electric currents or moving charges. He found that when a compass needle is near a live wire, the compass needle is deflected. When there is no current, the compass needle points north.

A compass needle is a magnet so it can be moved by a magnetic force. Where does the magnetic force (F) come from? Near the compass needle, there is a wire carrying an electric current so that the magnetic force must be exerted by the electric current.

Look at the picture on the side. The direction of the electric current and the direction of the magnetic field can be found using the right hand rule. If the electric current (I) moves up, the direction of the magnetic field (B) is as shown on the left, otherwise if the direction of the electric current is downward, the direction of the magnetic field is as shown on the right.

The magnetic field exerts a force on the current carrying wire

Previously it was explained that an electric current can exert a force on a magnetic compass needle. Can a magnet also exert a force on an electric current?

Suppose there is a wire carrying an electric current placed between the north and south poles of a magnet. The direction of the magnetic field is indicated by an arrow from the north pole to the south pole. If the direction of electric current (I) is indicated by a red arrow, then a magnetic force (F) appears whose direction is represented by a blue arrow.

The direction of the magnetic force F is perpendicular to the direction of the electric current I and perpendicular to the direction of the magnetic field B. The direction of the electric current, the direction of the magnetic field and the direction of the magnetic force can be determined using the right-hand rule.

The relationship between magnetic force, electric current and magnetic field is expressed by the following equation.

F = B I l sin θ

F is a symbol of magnetic force, B is a symbol of a magnetic field, I is a symbol of an electric current, l is a symbol of the length of a wire that is in a magnetic field.

θ is the angle between the direction of the electric current and the direction of the magnetic field. If the electric current is perpendicular to the magnetic field (90o) then the value of sin 90 = 1 so the formula changes to F = B I l, conversely if the electric current is parallel to the magnetic field (0o) then the value of sin 0 = 0 so that the magnetic force is 0.

To calculate the magnetic field, the formula above is changed to : B = F / I l.

The international unit for magnetic force is the Newton (abbreviated N), the International unit for magnetic field is the Tesla (abbreviated T). Tesla is named after the Serbian-American inventor and physicist, Nikola Tesla (1856-1943). Based on the magnetic field formula above, the magnetic field can also be expressed in units of Newtons per Ampere meter (N/A m). Besides Tesla, the magnetic field is also expressed in units of Gauss (G). Gauss comes from the name of the German mathematician, astronomer and physicist, Johann Carl Friedrich Gauss (1777-1855). 1G = 10-4T

The magnetic force on electric charges moving in a magnetic field

A magnetic field can exert a magnetic force on a current-carrying wire. Electric currents are electric charges in motion, so a magnetic field can also exert a magnetic force on freely moving electric charges, not just on conducting wires.

The formula for calculating the magnetic force on electric charges moving in a magnetic field is derived from the previous magnetic force formula F = B I l sin θ. Because I = q/t and l = v t, the magnetic force formula changes to

Description of the formula: F = magnetic force, B = magnetic field, q = electric charge, v = speed of motion of the charge, θ = angle between v and B

If v is perpendicular to B then θ = 90o , where sin 90o = 1. Conversely if v is parallel to B then θ = 0o, where sin 0o = 0. So the magnetic force is maximum when v is perpendicular to B and the magnetic force is zero when v is parallel to B.

The direction of the magnetic force F is perpendicular to the magnetic field B and perpendicular to the speed of the electric charge v.