explain gauss law for magnetic field
Answers
Answer:
Gauss Law states that the total electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux in an area is defined as the electric field multiplied by the area of the surface projected in a plane and perpendicular to the field.
Table of Content:
What is Gauss Law?
Formula
Gauss Theorem
Applications
Frequently Asked Questions
Problems
What is Gauss Law?
According to the Gauss law, the total flux linked with a closed surface is 1/ε0 times the charge enclosed by the closed surface.
∮E⃗ .d⃗ s=1∈0q .
For example, A point charge q is placed inside a cube of edge ‘a’. Now as per the Gauss law, the flux through each face of the cube is q/6ε0.
The electric field is the basic concept to know about electricity. Generally, the electric field of the surface is calculated by applying Coulomb’s law, but to calculate the electric field distribution in a closed surface, we need to understand the concept of Gauss law. It explains about the electric charge enclosed in a closed or the electric charge present in the enclosed closed surface.
Gauss Law Formula
As per the Gauss theorem, the total charge enclosed in a closed surface is proportional to the total flux enclosed by the surface. Therefore, If ϕ is total flux and ϵ0 is electric constant, the total electric charge Q enclosed by the surface is;
Q = ϕ ϵ0
The Gauss law formula is expressed by;
ϕ = Q/ϵ0
Where,
Q = total charge within the given surface,
ε0 = the electric constant.
⇒ Also Read: Equipotential Surface
The Gauss Theorem
The net flux through a closed surface is directly proportional to the net charge in the volume enclosed by the closed surface.
Φ = → E.d → A = qnet/ε0
In simple words, the Gauss theorem relates the ‘flow’ of electric field lines (flux) to the charges within the enclosed surface. If there are no charges enclosed by a surface, then the net electric flux remains zero.
This means that the number of electric field lines entering the surface is equal to the field lines leaving the surface.
The Gauss theorem statement also gives an important corollary:
The electric flux from any closed surface is only due to the sources (positive charges) and sinks (negative charges) of electric fields enclosed by the surface. Any charges outside the surface do not contribute to the electric flux. Also, only electric charges can act as sources or sinks of electric fields. Changing magnetic fields, for example, cannot act as sources or sinks of electric fields.
Gauss Law
Gauss Law in Magnetism
The net flux for the surface on the left is non-zero as it encloses a net charge. The net flux for the surface on the right is zero since it does not enclose any charge.
⇒ Note: The Gauss law is only a restatement of the Coulombs law. If you apply the Gauss theorem to a point charge enclosed by a sphere, you will get back the Coulomb’s law easily.
Applications of Gauss Law
1. In the case of a charged ring of radius R on its axis at a distance x from the centre of the ring. E = 14π∈0qx(R2+x2)3/2. At the centre, x = 0 and E = 0.
2. In case of an infinite line of charge, at a distance ‘r’. E = (1/4 × πrε0) (2π/r) = λ/2πrε0. Where λ is the linear charge density.
3. The intensity of the electric field near a plane sheet of charge is E = σ/2ε0K where σ = surface charge density.
4. The intensity of the electric field near a plane charged conductor E = σ/Kε0 in a medium of dielectric constant K. If the dielectric medium is air, then Eair = σ/ε0.
5. The field between two parallel plates of a condenser is E = σ/ε0, where σ is the surface charge density.
Gauss Theorem: The net flux through a closed surface is directly proportional to the net charge in the volume enclosed by the closed surface.
Φ = → E.d → A = qnet/ε0
- Gauss law for magnetic field states that the magnetic field B has divergence equal to zero, in other words, it is a solenoidal vector field. It is equivalent to the statement that magnetic monopoles do not exist.
- It is one of the four Maxwell's equations that underlie classical electrodynamics.
- Gauss' Law for magnetism applies to the magnetic flux through a closed surface. In this case, the area vector points out from the surface. Because magnetic field lines are continuous loops, all closed surfaces have as many magnetic field lines going in as coming out. Hence, the net magnetic flux through a closed surface is zero. Net flux ϕ = ∫B.dA = 0
- This means that the number of electric field lines entering the surface is equal to the field lines leaving the surface.
- The electric flux from any closed surface is only due to the sources (positive charges) and sinks (negative charges) of the electric fields enclosed by the surface. Any charges outside the surface do not contribute to the electric flux. Also, only electric charges can act as sources or sinks of electric fields. Changing magnetic fields, for example, cannot act as sources or sinks of electric fields.
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