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Electromagnetism formula list

27. Electromagnetism formula list

Coulomb's law

Coulomb 's law related to the static electricity can be expressed as "Power to work between charged particles is proportional to the product of electric charge, and inversely p proportion to the power 2 of the distance between the electric charge". If we assume the charge amount of the 2 point charge as Q1,Q2 [C], distance as r [m] between electric charge, and the size of the electrostatic force that works on both the electric charge as Coulomb's force F [N] then Coulomb's law is expressed by the following formula. When F is positive, it becomes repulsion force, when negative it becomes attracting force.

shows dielectric constant within the vacuum, and shows relative permittivity of material.

Gauss's law

Gauss's theorem states that "the sum total of the in and outward electrical flux line through a closed surface is equal to the 1/ε total amount (ε is the dielectric constant) of the electric charge inside the surface". It can be expressed by the following formula. In the formula, the sum total of electrical flux line is obtained by integrating the electrical field E, passing the entire surface area, that is same dividing the total amount of internal electric charge Q by the dielectric constant ε.

Further, Gauss's theorem can be expressed as follows by using dielectric flux density 、 charge density


Capacitance is the amount of how much electric charge can be stored in an insulated conductor. Symbol used is C, and the unit used is farad [F]. The capacitance is 1 farad when an electric charge of 1 coulomb can be stored in when a voltage of 1 volt is provided in a material. The capacitance of an isolated conductor is given by the following formula when capacitance is C [F], electric charge stored in the conductor is Q [C], and a potential based on an infinite distance V [V].

Capacitance between the parallel plate is given by the following formula when the area of the plane is , the distance between the plane is d [m], relative permittivity of the dielectric between the the plane is .

The energy stored in the capacitor (electrical energy) W [J] is capacitance C [F], and when the voltage between the terminals is V [V], then the formula is given as follows.

Magnetic field intensity

The definition of intensity and direction of the Magnetic field is "It is assumed that there is infinitely-long bar magnetic where the effect of south pole is negligible within the magnetic field, the amount of force in each 1[Wb] of north pole is considered as strength, and the direction of the force is considered the direction of of the magnetic field". Therefore, relation between the force F [N] on magnetic charge m [Wb], and the electric field H [A/m] is given by the following formula.

Further, the Magnetic field intensity H [A/m] at the point r [m] separated from the magnetic charge m [Wb] is proportional to the strength of the magnetic charge, and inverse proportional to the distance, it is defined by the following formula.

Here, is permeability inside vacuum magnetic constant, and is relative magnetic permeability of material.


In Self-inductance, the magnetic flux alters wherein the coil penetrates the current when the current that flows in the winding wire alters, and electro motive force is generated in the direction which deny the alteration of magnetic flux. This electro motive force is called back electromotive force since it generates on the direction that prevents the alteration of current, it is expressed by the following formula when Self-inductance is considered L [H], and the current of winding wire is I [A].

Self-inductance shows the self-inductability when the current is made to vary ,and is given by the following formula.

Electric field intensity

The electrical field is a field of an electric which occurs on the surroundings of the electrically-charged object. The definition of its strength and direction is "the size of the force that works on it is considered the strength when a positive electric charge is placed within the electric field, and the direction of the force is the direction of the electric field". Therefore, the relation between the electrostatic force F [N] , and the electrical field E that work on point the point charge Q [C] is given by the following formula.

For example, the strength of the electric field at a point r [m] separated from the point charge Q [C] can be obtained by the following formula.

Electric potential and potential difference

The potential within an electric field is an electrical potential energy which has unit positive electric charge in a target point, and is the work [J/C] to bring the positive electric charge from the unit positive electric charge to the point. Moreover, and the potential difference is the necessary work to transfer the unit positive electric charge from one point to the other one point. Unit is used as Volt [V], and and 1V is defined as the potential difference to do the work of 1J by the electric charge 1C.


Between the material and magnet such as iron that is kept near the magnet, magnets, the same type of North South magnetic pole works on repulsive force and heterogeneous North South magnetic pole works on attracting force. Magnetism is proportional to the product of the strength of the respective magnetic charge, and is inversely proportional to the square of the distance. The magnetism F [N] that works between the point of mutual magnetic charge place within the material can be given by the following formula when the respective strength of magnetic charge point is M1, M2 [Wb], and the distance between the magnetic charge point is r [m], the permeability of vacuum magnetic constant is μ0, and the relative magnetic permeability of the material is μr.

The positive negative electric charge can be thought as a unit in case of static electricity, the magnetic charge generally exists in the form of magnetic dipole wherein paired as N and S.


When the magnetic flux that passes through the winding wire varies, inductors generate an opposing voltage proportional to the rate of change in current in a circuit. It can be expressed by the following formula when number of turns of the winding wire is considered N, magnetic flux is Φ and electro motive force is e.

This variation of magnetic flux can be provided by itself or by other coil. The former is called as Self-inductance and the latter is called mutual inductance.

Mutual inductance

The change of magnetic flux by the variation of current of the other coil will bring induced electromotive force in the other coil when the 2 coils are electromagnetically combined. The extent to show this combination is called mutual inductance M [H] and is given by the following formula.

L1, L2 is the Self-inductance of the respective coil, k is the binding coefficient and takes the value of 0 to 1. The induced electromotive force by the mutual inductance can be expressed by the following formula when the current of one of the coil is I1 [A], and the electro motive force of one of the other coil is e2 [V].