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Gauss’s Law is a fundamental law of electrostatics that helps to explain electric fields. It states that “the net electric field at any point is proportional to the total charge enclosed by a closed surface.”
We can explain Gauss’s Law in detail with the following example: Imagine an electric wire with an infinite length. The wire has two parts, one part being positive and the other negative.
First, take the electric field for each point charge and set them equal to find whether the electric field is zero. Hence, they will cancel each other out, and the electric field will be zero.
Electric Field Due to Infinite Wire
Gauss’s Law can help you to calculate this electric field. Gauss’s Law, the electric flux through a closed surface is equal to the total enclosed charge divided by the electrical permittivity of the vacuum. For example, Gauss’s Law calculates the electric field produced by a charged conducting sphere. You have a charge surrounded by a spherical surface in such an instance. To calculate the overall flux, multiply the electric field intensity at the sphere’s surface by the sphere’s surface area.
Have you ever wondered about the electric fields surrounding an infinite wire? It is a famous problem in physics: How do you calculate the electric field due to an endless wire?
This article will explore finding the electric field around an infinite wire using Gauss’s Law.
Similarly, we can use Gauss Law in finding fields due to infinite wire by considering cylindrical gaussian surfaces and applying the law. We will also learn how to use it to solve some interesting problems, like finding the electric field generated by a charged particle sitting on an infinitely long piece of metal.
Infinite wire example
- A simple and illustrative example of Gauss’s Law is an infinite wire.
- The wire has a charge uniformly distributed along its length, and this means that from any point on the wire, there will be a uniform electric field pointing away from the wire.
Finding the electric field due to an infinite wire
Gauss’s Law is a mathematical equation that predicts the electric field at any point due to an infinitely long wire. Gauss’s Law finds the electric field of any wire shape.
To find the electric field, you need the following:
- The electric current
- The length of the wire
- The cross-sectional area of the wire
Consider a wire with an evenly distributed charge along its length. The wire is infinite. This means that there will be a uniform electric field pointing away from the wire from any point on the wire.
To find the magnitude of this electric field, we can use the equation:
This equation shows that a larger 0 increases E, so the air has a more dielectric constant than water.
According to Gauss’s Law:
Gauss’s Law
Gauss’s Law is a law in electromagnetism that says there is an electric field around any point charge, and the magnitude of the field is proportional to the amount of charge.
Consider a positive point charge (Q) at location r. Then, we can determine the magnitude of this field with the equation:
Conclusion
With Gauss’s Law, we can find the electric field (or force felt by an electric charge) due to an infinite wire. The electric field is proportional to the number of charges, the distance of the charge from the wire, and the electric field constant. We will find the electric field due to an infinite wire with a charge density of d per metre and a distance of L metres from the wire. The electric field from this wire would be inversely proportional to distance.
