The Difference Between Electrostatics and Magnetostatics

February 18, 2022

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Key Takeaways

Electromagnetic fields can be defined as the combination of electric and magnetic fields.
Electrostatics can be referred to as a branch of physics that studies current free charge distribution.
Magnetostatics is the branch of physics that deals with the stationary current distribution and its associated magnetic fields, which are independent of electric fields.

Electrostatics deal with electric charges at rest

The electrostatic spray method utilizes electrostatically charged epoxy powder, and the adhesion is strong when there is a charged interaction between the copper and the powder. This is an application of electrostatics. Electrostatics is a specific case of electromagnetism where there are no moving electric charges. Similarly, one can say magnetostatics is another special case of electromagnetism, where there are no time-dependent currents.

If we consider electrostatics and magnetostatics as excerpts of electromagnetism, we can say the former deals with electric fields and the latter deals with magnetic fields. But, both fields are not a function of time. There are a variety of conceptual differences between electrostatics and magnetostatics. In this article, we will explore some of the basic concepts as well as the differences between electrostatics and magnetostatics.

Electromagnetism, Electrostatics, and Magnetostatics

Electromagnetism is the branch of physics studying electromagnetic fields. Electromagnetic fields can be defined as the combination of electric and magnetic fields. The electric and magnetic fields are coupled and time-varying. Electromagnetic fields can be described using Maxwell’s equation:

As per Maxwell’s equation, a time-varying magnetic field doesn’t exist without a simultaneous electric field and vice versa. In the above set of Maxwell’s equations, the time derivatives become zero under static conditions. Considering Maxwell’s equations under static conditions, reduce the four coupled equations into two uncoupled pairs of equations. Each pair corresponds to electrostatic fields and magnetostatic fields, respectively. The decoupled equation proves that electrostatic fields can exist without the presence of magnetic fields and vice versa.

Electrostatics

Electrostatics can be referred to as a branch of physics that studies current free charge distribution. It deals with electric charges at rest, which is called the Coulombian approach. The charges at rest obey certain laws, such as like charges repel, unlike charges attract, and charged objects attract neutral objects. From Maxwell’s equations, the decoupled equations corresponding to electrostatic field conditions can be derived as follows:

Decoupled equations

The electrostatic field is established between two point charges and the force between the charges can be derived from Coulomb’s law.

The stationary or static charges produce time-invariant electric fields, otherwise called electrostatic fields. The electrostatic fields can be derived from Coulomb’s law, which defines the force between two charges at rest. The electrical interactions between the charges at rest are different from moving charges. Therefore, electrostatics can be regarded as the opposite of electrodynamics.

When the charges are uniformly moving, then the electrical interactions are different from that of static charges. Let’s discuss the physics of uniformly moving charges in the upcoming section.

Magnetostatics

The electric charges in uniform motion produce stationary electric current distribution and magnetic effects. The current distribution and magnetic field produced are independent of time. Magnetostatics is the branch of physics that deals with the stationary current distribution and its associated magnetic fields, which are independent of electric fields. It can be summarized as the study of magnetic fields produced by direct currents or permanent magnets, and is called the Amperian approach. There is no time derivative of current in magnetostatics. From Maxwell’s equation, the decoupled equations corresponding to magnetostatics can be derived as follows:

Decoupled equations for magnetostatics

Magnetostatics covers the magnetic fields, which are independent of the electric field, but not limited to the magnetic fields associated within the various spatial distributions of steady current, the energy associated with magnetic fields, and the inductance property that helps in storing magnetic fields.

The Difference Between Electrostatics and Magnetostatics

In the macroscopic world, the impact of electrostatic forces is small and difficult to measure. There is electrostatic force between two static charges, but the strength is much less than gravitational forces. Therefore, its influence on macroscopic bodies is small. But, when it comes to particles of sizes 1-100 µm, the electrostatic force is high compared to aerodynamic and gravitational effects.

When static charges start to move, electrostatic forces and additional magnetic forces get exerted between the charges. The magnetic force is so small that it is difficult to measure. However, the force exerted by the organized motion of a vast number of electrons--generally called electric current--is possible. The electric current is an atomic level characteristic and exists even in electrically neutral materials. It is possible to measure magnetic force independent of electric force.

The definitions of the quantities associated with electrostatics and magnetostatics differ. Both electrostatics and magnetostatics obey the duality principle. However, the definition of each quantity is different in electrostatics and magnetostatics. The table below differentiates the electrostatic and magnetostatic quantities.

Quantity	Electrostatics	Magnetostatics
Sources	Static charges	Steady current and permanent magnets
Force on charge	F=qE	F=qv x B
Field intensity	E(V/m)	H(A/m)
Flux density	D (C/m2)	B (T)
Material relationship	D/E=(permittivity)	B/H=u(permeability)
Energy storage property	capacitance	inductance

Comparison of electrostatic and magnetostatic quantities

Electrostatics and magnetostatics deal with the aspects of electromagnetic theory where the sources of the electric field and magnetic field are time-invariant. Even though both deal with time-independent fields, there are differences in electrostatics and magnetostatics that derive them as two different branches--subsidiaries to electromagnetic theory.

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