What is Electric Charge, Electric Field and Magnetic Field - It's Introduction, Mathematical Expressions,

Electric charge:

Think of electric charge as a fundamental property of matter. Just as mass causes gravity, charge causes the electric force. This force has two types: positive charge and negative charge.

Inside an atom, the center i.e. nucleus, has protons and neutron. Protons have a positive (+) charge and neutron has no charge, it's neutral. In outer cloud, little particles called electrons revolves around the nucleus. Electrons have a negative (-) charge. In a normal, neutral atom, the number of protons (+) equals the number of electrons (-). The opposite charges cancel each other out, so the atom has no net charge.

When atom has lack of electrons and more protons than electrons, then it has positive charge. When atom has excess of electrons and more electrons than protons, then it has negative charge.

A positive charge pushes away other positive charges but pulls on negative charges. A negative charge pushes away other negative charges but pulls on positive charges. This push and pull is the engine behind almost everything we call electricity.

Electric Field:

Imagine you have a charged object, say a balloon that you've rubbed on your hair giving it a negative charge. Now, if you bring another charged object like a
positively charged object near it, you'll feel a force, either an attraction or a repulsion. How does the balloon push or pull the other object without touching it?
The answer is the electric field.

The electric field is a condition or a state of the space around a charged object. Think of the electric field as an invisible influence that a charged object creates in the space around it. Every charged object generates an electric field around it. It's there even if there's no other charge to feel it. We can't see it, but we can detect its effects. The field is the mechanism by which the charge exerts force on other charges without any physical contact.

This field is what transmits the electric force through space, telling other charges which way to push or pull. When you place another charge in the
electric field, the field exerts a force on
that charge.
 

How to visualize the electric field?

A common way to visualize the electric field is to think of it as a field of arrows. The direction of the electric field at a point is the direction a positive test charge would move if placed at that point. So, if you have a positive charge, the electric field arrows point away from it because a positive test charge would be repelled. If you have a negative charge, the arrows point toward it because a positive test charge would be attracted. For a single positive point charge, the electric field lines radiate outward. For a negative point charge, the field lines point inward.

The strength or magnitude of the electric field is represented by the density of these arrows. Closer to the charge, the field is stronger, so we draw more arrows. Further away, the field is weaker, so fewer arrows.

The Electric Field is a Vector Field

This means that at every point in space, the electric field has both a magnitude i.e. how strong and a direction i.e. which way a positive charge would be pushed.

How we can imagine electric field is looks like?

Let's consider a few cases:

• A single positive charge:

The field lines radiate outward from the positive charge.

• A single negative charge:

The field lines radiate inward toward the negative charge.

• Two positive charges:

The field lines start on each positive charge and go outward, but they repel each other in the middle so the lines from the two charges will repel each other. Imagine the lines from each charge curving away from the other charge.

• Two negative charges:

Similar to two positive charges, but the lines end on the charges and the pattern
is the same as for two positives but with arrows pointing inward.          

• A positive and a negative charge:

The field lines start at the positive, curve around, and end at the negative. In the middle, the field lines are roughly straight from the positive to the negative. Some lines go directly from positive to negative, but others curve around the sides.

Magnetic Field:

Imagine you hold a simple compass. The needle always points north. Why? Because the Earth is surrounded by a magnetic field. The needle, which is a small magnet itself, aligns with this invisible field.

A magnetic field is a region of space where a magnetic force can be felt. It is created by moving electric charges i.e. current, magnetic materials like a bar magnet and by a changing electric field. The field is detected by the force it exerts on other moving charges or magnetic materials.

It is a vector field, meaning it has both a magnitude or strength and a direction at every point in space. The direction of the field line at any point shows the direction a north pole of a compass would point. Field lines always emerge from the North pole and enter the South pole. The density or closeness of the field lines indicates the strength of the field. The closer the lines, the stronger the field.

An electric field exerts a force on any charge, whether it's moving or stationary. But magnetic field only exerts a force on moving charges and magnetic poles. A stationary charge feels no force from a magnetic field. Magnetic field lines always form continuous closed loops. They have no beginning or end. This is different from electric field lines, which start on a positive charge and end on a negative charge.

The force a magnetic field exerts on a moving charge doesn't simply push or pull, it pushes sideways. The force is always perpendicular to the velocity, it acts as a centripetal force, causing a charged particle to move in a circle. It does no work on the particle, it can change the particle's direction but not its speed or kinetic energy.

We use the right hand rule to find direction of this force, by pointing your fingers in the direction of the velocity (v) of a positive charge. Then curl your fingers towards the direction of the magnetic field (B). Your extended thumb now points in the direction of the force (F).

This force is given by the formula,
F = q(v × B)

Where,
F : Magnetic Force (Newtons, N)
q : Charge (Coulombs, C)
v : Velocity vector of the charge (m/s) B : Magnetic Field vector (Tesla, T)


There are two primary sources:

1. Moving Electric Charges (Current): 

This is the most fundamental source. An electric current flowing through a wire creates a circular magnetic field around it, described by the right-hand grip rule: if you grip the wire with your right hand with your thumb pointing in the direction of the conventional current (+ to -), your curled fingers show the direction of the magnetic field lines.

2. Fundamental Magnetic Dipoles: 

At the subatomic level, the spin and orbital motion of electrons create tiny magnetic fields. In most materials, these cancel out. In ferromagnetic materials like iron, nickel, and cobalt, these tiny fields can align to create a permanent magnet.

Why stationary charges create electric field, but how moving charges create magnetic field?

By classical or experimental perspective:
It's an experimental fact described by the Biot-Savart Law. The motion of charge (v) is the direct source, and the resulting field is perpendicular to that motion.

By relativistic perspective:
The magnetic field isn't a new field created from nothing. The magnetic field is the electric field in motion. It is relativistic consequence of the electric force. Imagine a single, stationary positive charge. It creates a purely radial, outward electric field. Now, you start moving past this charge at a constant velocity. According to Einstein's theory of Special Relativity, from your moving reference frame, it is as if you are stationary and the charge is moving past you.

From your moving perspective, the space in the direction of the charge's motion appears to be contracted. This slight length contraction means the distribution of the electric field lines from the moving charge is no longer perfectly symmetrical. The field lines become bunched up perpendicular to the direction of motion. What we observe and label as a magnetic field is actually a direct consequence of this transformed electric field. It's the electric field in motion. So, in a very deep sense, the magnetic field is the way the electric force behaves when the sources of that force are in motion relative to the observer. What one observer sees as a pure electric field, a moving observer will see as a mixture of an electric and a magnetic field.

Stationary charge creates only an electric field (E). While moving charge creates both an E-field and a Magnetic Field (B).

How permanent magnets create both magnetic and electric field?

Electromagnets create both magnetic and electric field because we run electric current through wire. Permanent magnets don't have net charge flow like electromagnets do. But for permanent magnets, it's not about macroscopic charge flow it's about the intrinsic property of electron spin at the atomic level.

The primary moving charge responsible for the magnetic field in a permanent magnet is the electron, a negative charge. Inside every atom, there are two ways electrons create a tiny magnetic field.

One is orbital motion, in which electrons orbiting the nucleus act like a tiny loop of electric current. A current loop creates a magnetic field.
Second is electronic spin, which is the dominant effect in permanent magnets like iron. Think of electrons as tiny, spinning balls of charge. This spinning motion also makes them act like tiny magnets, each with a north and south pole. This is an intrinsic quantum property.

In most materials like plastic, these tiny electron magnets point in random directions, so their magnetic fields cancel each other out. In ferromagnetic materials like Iron, Nickel, Cobalt, something special happens. Large groups of electrons in regions called magnetic domains can have their spins align in the same direction. When these domains are aligned, the tiny magnetic fields from each electron add up to create a strong, net magnetic field for the entire object. This is what makes a permanent magnet.

Here, the current isn't a flow of charge from one end of the magnet to the other through the air. The currents are the internal, atomic motions of the electrons, their spin and orbital motion. We can model the net effect of all these aligned atomic currents as imaginery current running on the surface of the magnet. Inside the magnet, this current flows in a direction that creates the magnetic field from south to north. The magnetic field lines themselves are continuous closed loops that emerge from the North Pole, travel through the air outside the magnet, and re enter at the South Pole, completing the loop inside the magnet.

To create a magnetic field in non magnetic materials like copper, wood, plastic. In these materials electron spins are randomly oriented and cancel each other out. There is no net magnetic field from the material itself. To create a magnetic field, charges should move in a coordinated, net direction. This is an electric current. To make electromagnet, take a coil of copper wire which is non-magnetic material and connect it to a battery. The battery pushes electrons, creating a current. This current generates a strong magnetic field. When you disconnect the battery, the current stops, and the magnetic field disappears.