Electric Field

Electric Field

Let us see, what is field? Consider a magnet. it has its own effect in a region surrounding it. The effect can be experienced by placing another magnet near the first magnet. Such an effect can be defined by a particular physical function. In the region surrounding the magnet, there exists a particular value for that physical function, at every point, describing the effect of magnet.
So Field can be defined as the region in which, at each point there exists a corresponding value of some physical function.
Let us study What is this Electric Field?
We know that there are generally two types of charges existing in nature:

1. Positive
2. Negative.

Such an electric charge produces a field around it which is called an electric field.

To generalize the definition of electric field considers that a very small test charge q₀ is placed near to the object carrying much higher positive charge having value Q₀.

Electric field or the strength of the electric field produced by the object having charge Q₀ on the positive test charge q₀ is defined as the Electric force per unit charge.

|E| = ForceCharge = Feq0.

Where F_e= Force due to the charge q_o
q₀= Test Charge coming in the electric field.
Thus Electric field E is defined as ratio of the electric force acting on the positive test charge q₀ and divided by the magnitude of the positive test charge.

Electric Field Equation

The Electric field E is defined as ratio of the electric force acting on the positive test charge q₀ and divided by the magnitude of the positive test charge.The Electric field formula is given by:
|E| = Feq0Where |E| is the Magnitude of Electric Field is considered,
F_e is the electric force acting on the positive test charge,
q₀ is the positive test charge.

Note that electric field considered above is produced by the charge which is external to the test charge q₀ and not by the positive charge itself.
Electric field is the property of the source for example every electron come within its electric field.
The above formula is used in Calculating Electric Field at a point.

Electric Field Units

Units of the electric field can be determined from the formula of the electric field defined above.
|E| = ForceChargeTherefore as SI unit of force is Newton and SI unit of the charge is Coulomb.
Unit of electric field will be N/C.

Electric Field Direction

To determine the direction of the electric field consider that charge Q and q₀ i.e. positive test charge are present. Now the electric force between the charge Q and the q₀ is given by the Coulomb force.

The force between the charges Q and q₀ is given by the formula as

F = ke(|Q||q0|)r^d2.Where
F = Electrostatic force between two charges
d = distance between Q and q₀
Q, q₀ = Electrostatic charges.
k_e = Coulomb constant.
And r^ is the unit vector directed from the charge Q towards the test charge q₀.
According to the electric field formula

E = Feq0substituting the value of force F_e, we get
E = ke(|Q||q0|)r^(d2q0)
Thus Electric Field formula is given by
E = ke(|Q|)r^d2.

Here E is also termed as the Electric Field Intensity. Note that the electric field is a vector quantity as it has both magnitude and the direction associated with it.

The Electric Field Strength produced by charge Q is given by

E = ke(|Q|)r^d2. Therefore the direction of the electric field produced by the charge Q is radially outward if the charge Q is positive and the electric field produced by the electric charge Q is radially inward if the charge Q is negative.

Electric Field Lines

Electric Field Lines are produced by the negative charge as shown in the figure below.
They are nothing but a way of pictorially mapping the electric field around a configuration of charges. It is the curve drawn in such a way that the tangent to it at each point is in the direction of the net field at the point. An arrow on the lines of force is a must to indicate the direction of the electric field.

In space, electric field is produced by the charges. Electric field lines are drawn to signify the direction of the electric field and the strength of the electric field at various points in space.

Electric Field Potential

Electric potential at a point is defined as the amount of work done in bringing unit positive charge from infinity to that point. Electric potential is a scalar quantity.
Electric field potential or Electric Field Voltage at a point is equal to the electric potential energy of a charged particle at that location divided by the charge particle.

Electric potential at a point P due to charge Q is given by
V = 14πϵ0 Qrwhere Q is the charge
r is the distance between the charges
ϵ0 is the permittivity in free space.
it is also termed as the Electric Potential or the Electrostatic Potential. The Unit of electric field potential is Joules per Coulomb.

Dipole Electric Field

The system in which two charges of equal magnitude but of opposite sign separated by the distance d are present is termed as a dipole. Electric dipole moment is represented by P.P is equal to the product of the charge q present in the dipole and the distance d between the two charges of the dipole.

The Formula for Electric dipole moment is given by
E= |qd|Where P is a vector quantity.
Direction of the electric dipole moment is from the negative charge to the positive charge present in the dipole. The field which is produced inside the dipole is given in the figure below.
In the figure shown below note that the electric field is shown in direction radially outward from the positive charge of the dipole and radially inward in case of the negative charge of the dipole.
E = 12πϵ pd3.

Electric Field inside a Sphere

The electric field inside a sphere can be found by considering that the sphere is uniformly charged and also considering a hypothetical sphere inside it with radius r which is less than the radius R of the charged sphere.
Hence we have
∮E⃗ .da→ = Qenclosedϵ0As the electric field is emerging outside and hence is constant, so the integral will become
E⃗ ∮da→ = Qenclosedϵ0The integral of the da is area of the sphere and the total charge enclosed is given by the sum of the point charge and the product of the volume of the sphere and the charge density and hence
E(4 π r² ) = Q+ρ(43πr3)ϵ0.So the electric field inside the sphere which is uniformly charged is given as below
E = Q+ρ(43πr3)4πr2ϵ0.Here E is the electric field inside the sphere
Q is the net charge on the sphere
r is the radius of the sphere.

Electric Field of a Wire

The electric field inside the wire having uniformly distributed charge can be derived by using the gauss law. The configuration of the wire is shown in figure below.

The electric field produced by the charged wire has the cylindrical symmetry. The surface of the cylindrical symmetry is considered as the Gaussian surface.

Electric Field Capacitor

Electric field between two parallel plates of the capacitor is defined as the ratio of the charge density to the permittivity.

E = σϵ0where σ = Charge density,
ϵ = Permittivity of free space
= 8.854 × 10^-12 F/m.

Where charge density is defined as the ratio of the charge per unit area.
This is the net electric field produced inside the capacitor charged plates.

Net Electric Field

The Net electric field is defined as the total field experienced by a point under the various charges in the system. To understand it better we will look at the problems below.
Let us consider the following charges q₁, q₂, q₃, ............. q_n.

so the Net electric field is given by
q = q₁ + q₂ + q₃ + q₄ + ...... +q_n.

Uniform Electric Field

The uniform electric field is the electric field which is not changing with respect to time. It is constant and not varying.

Uniform electric field is defined as an electric field which maintains the constant charge over the entire field.
Consider the parallel plate capacitor, we could see the electric field is same at all point from positive end to the negative end.