Relation between Electric Fields and Magnetic Fields

Relation between Electric Fields and Magnetic Fields

Brief visualisation

Try to imagine a vertical long wire carrying current in which charges move with a certain velocity say v which is kept parallel to an observer standing on the ground say O1. There is no electric field, but there is a magnetic field which exerts a force on the charge and therefore the charge is attracted towards the wire due to magnetic force. Now let say another observer O2 who is moving at a uniform velocity v parallel to the wire. If we see through his frame of reference, the moving charges in the wire are at rest for him and hence, the magnetic field (if present) cannot exert any force on the charge.  However, the observer O2 also sees that the charge is attracted by the wire although that charge is at rest for him.

In fact, the acceleration of the charge is the same for both O1 and O2 since they are unaccelerated with respect to each other. Hence, there must be an electric field in the frame of O2, which was a pure magnetic field in the frame of O1 which eventually turns out to be a combination of electric field and magnetic field in the frame of O2.

Actually, they both are two different aspects of the same entity, electromagnetic field. Whether the electromagnetic field will look like an electric field or magnetic field, it depends on the frame from which we are looking at the field. In classical physics, usually, we treat them differently for a given frame of reference.

Electric Field and Magnetic Field

Before getting deeper, let’s talk about the electric field. Assume a charge kept at rest in space. Now if we bring another charge (also known as test charge) close towards the first charge, electrostatic force starts acting between them. To calculate force experienced by charge easily, we need to define a quantity Electric Field which is given by the equation F = qE. Where ‘E’ represents an electric field due to the first charge. Now, it becomes easy for us to calculate the electrostatic force between the two charges from the given equation.

You can define the magnetic field as a force field which is formed due to moving electric charges and magnetic dipoles.

Faraday’s Law and Maxwell’s law;

If we go through the Faraday’s Law according to which an electric field can be generated by moving magnetic field and also via Maxwell’s correction to Ampere’s Law, the magnetic field can be produced as well by changing electric field.

Special theory of relativity;

According to the Einstein’s special theory of relativity, the partition of electromagnetic force into separate electric and magnetic components is not fundamental, rather varies with the frame of reference of observation. The Same field may be electric or magnetic or mixture for different observers.

Talking formally, the speacial theory of relativity combines the electric and magnetic field into a ran-2 tensor, called electromagnetic tensor. This component gets mixed due to change in reference to observation.

Quantum Electrodynamics;

In modern physics, the electromagnetic field is understood to be not a classical field, rather a quantum field. Rather than representing it as a vector, it is represented as a vector of three quantum operators at each point.

We calculate the magnitude of electromagnetic interactions between the charged particle and their antiparticles using perturbation theory where virtual photons are exchanged.

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