Electric field and its mathematical form

The electric field is a fundamental concept in physics that describes the influence of a charged object on the space around it. It is a vector field, meaning that at every point in space, it has both magnitude and direction. The electric field is denoted by the symbol $E.$

Definition of electric field

The electric field at a point in space is defined as the force per unit positive charge experienced by a small test charge placed at that point. Mathematically, it is expressed as the force ($\mathbf{F}$) experienced by a positive test charge (q0​) divided by the magnitude of the test charge.

Electric Field Equation

[math]\mathbf{E} = \frac{\mathbf{F}}{q_0}[/math]

The electric field is measured in units of volts per meter (V/m).

Direction of electric field

The electric field points in the direction of the force that a positive test charge would experience if placed at that point. In other words, the electric field lines point away from positive charges and toward negative charges.

Superposition Principle

The electric field is a vector quantity, and it obeys the superposition principle. This means that the net electric field at any point in space due to multiple charges is the vector sum of the individual electric fields produced by each charge.

Coulomb’s Law and Electric Field

There is a relationship between Coulomb’s Law and the electric field. For a point charge $Q$, the electric field ($\mathbf{E}$) at a distance $r$ from the charge is given by

[math]\mathbf{E} = \frac{1}{4 \pi \epsilon_0} \frac{q}{r^2} \hat{\mathbf{r}}[/math]

Where:

• $k$ is Coulomb’s constant (8.9875×10^9 N m^2/C^2,
• $Q$ is the magnitude of the point charge,
• $r$ is the distance from the charge,
• [math]\hat{\mathbf{r}}[/math] is a unit vector in the direction from the charge to the point in space where the electric field is being measured.

Electric Field Lines

 Electric field lines are a visual representation of the electric field. They show the direction of the electric field at each point and are directed away from positive charges and toward negative charges. The density of field lines indicates the strength of the electric field, with closer lines representing a stronger field.