Magnetism and Gauss’s Law

Magnetism and Gauss law are two of the most crucial concepts introduced in Physics. Magnetism helps you understand the most fundamental interactions in nature which is the interaction between the moving charges. For example, like the electrostatic force and the gravitational force, the magnetic force can be termed as an interaction at a distance. According to the Gauss law, the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux can be defined as the electric field multiplied by the area of the surface projected in a plane and perpendicular to the field.

In this article, we will be explaining one of the most crucial chapters of physics which is magnetism and Gauss’s Law.

Introduction to Gauss’s Law in Magnetism

According to the Gauss law, the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux can be defined as the electric field multiplied by the area of the surface projected in a plane and perpendicular to the field. A magnet has the property to repel or attract other substances. 

Gauss Law in Magnetism 

Introduced in the year 1835, Carl Friedrich Gauss stated that Gauss’s Law in Magnetism is related to a net magnetic flux of all closed areas that will be equal to Zero.  

Gauss Law in magnetism can be defined as the magnetic flux through a closed surface. In this, the area vector points out from the surface. Since the magnetic field lines are in a continuous loop, all closed surfaces have as many magnetic field lines going in as coming out. As a result, the net magnetic flux is described as zero. In mathematical form this is written as

 ∫B⋅dA = 0

Here B is the magnetic field vector and dA is a small element of surface area vector.

Gauss’s Law in Electrostatics

According to Gauss’s Law in electrostatics, the electric charge within the imaginary Gaussian or the closed surface is equal to 1 time of the net electric flux through any closed surface. The Gauss law of electrostatics is written as ∫E⋅dA=Q/ε0 

Where,

• E is the electric field vector
• Q is the enclosed electric charge
• ε0 is the electric permittivity of free space
• A is the outward pointing normal area vector

Define Electrostatics and Electric Field 

Electrostatics in Physics can be defined as the electric charges which are either moving slowly or are stationary, which means they have significantly less acceleration as compared to the static charges. 

The electric field can be defined as when a single charged particle has the ability to excrete force to the extent that other non-charged particles can feel its force. This is often termed the electric field. The electric field is a vector meaning it consists of both directions and the magnitude. Lines of force are differentiated based on positively or negatively charged particles. If it is positively charged, the force line will be directed outwards. However, it will be directed inwards for a negative charge. 

Applications of the Gauss’s Law 

Generally, there are three major applications of Gauss’s Law: firstly, the complex electrostatic problems can be easily tackled through Gauss’s Law. It involves symmetries including spherical, planar, or cylindrical symmetry. Apart from this, there are also instances where the electrical field calculation is complex. Also, Gauss’s Law is used to simplify the process of evaluating the electrical fields. Applications of Gauss’s law are as follows- 

• The intensity of the Electric Field because of the plane sheet

If considered the infinite charged sheet, the Gaussian surface in a cylindrical shape is termed in a way that the surface is perpendicular to electric fields. In this case, the lower part of the surface of the Gaussian will only consist of electric flux.

• The intensity of the Electric Field because of the spherical sheet 

Imagine a positively charged circle with radius R where (q) is distributed all around the circle evenly. For the calculation of the electric field, a Gaussian surface that is spherical in shape is considered. 

1. Electric field out of the shell – For the calculation of the Electric field out of the shell, it is considered the radius of the shell (R) is smaller than the Gaussian surface radius or (R < r). 
2. The electric field in the charged shell – To calculate the Electric field in the charged shell, it is assumed the Radius of the shell R is greater than the radius of the Gaussian surface or (R > r). 
3. Electric field on the shell surface – To calculate the Electric field on the shell surface, it is assumed that the radius of the shell is equal to the radius of the Gaussian surface or (R = r). 

Magnetostatics 

Magnetostatics is another important concept in electricity. It is one of the significant studies of magnetic fields. According to Magnetostatics, the current remains steady or does not change with time. This law is known as the Biot- Savart’s Law. 

Ampere’s law 

Ampere’s law helps in the calculation of the magnitude of magnetic field lines. As studied till now, the gauss theorem is related to the electric field lines; however, Ampere’s law strictly talks about the magnetic field lines. This magnetic field is associated with the electric current, stating that the electric field never changes as time passes. 

Conclusion 

In this article, we learned about Gauss’s law. Gauss’s law can be used in electrostatics and magnetostatic. Gauss’s law is used to find out vector field flux passing through a surface. These vector fields are electric field and magnetic field.