Electric Field due to a Point charge, Charged Ring and Continuous Charge

So there is only x component.

The electric charge distributions are as shown below

The filed due to plane y = 
The field due to plane x = 
The field due to line charge 
is the unit vector along perpendicular to the line charge passing through P.

Concept:

The electric potential due to a point charge is given by:

where, V = Electrical potential 
Q = Point charge
d = Distance from charge
ϵ_o = Permittivity of free space
The relationship between potential and electric field intensity is:
E = V/d

Explanation:

From the above expressions, the electric potential is:

• It is directly proportional to the magnitude of the charge.
• It is inversely proportional to the distance from the charge.
• It is independent of the relative permittivity of the medium in which the charge is placed but inversely proportional to the permittivity of free space.
• It is directly proportional to the electric field intensity.

Concept:

The magnitude of electric field intensity at a point P due to infinitely long uniform charge density λ is

r → the perpendicular distance from the point to the infinitely long charge density

Analysis:

Here, the point (0, 5, 1) and (2, 5, 1)

r is the same and is equal to

∴ the electric field will be same in both the cases.

Electric flux lines originate from positive charges and terminate at negative charges as shown:​

Note: It is the magnetic field lines that form a closed loop as shown:

According to Coulomb's law, the electric field due to a point charge q at a distance r is given by E = (kq)/(r²), where k is the electrostatic constant.

Due to the symmetry of the charged ring, the electric field vectors produced by each element of charge on the ring cancel each other at the center. Therefore, the net electric field at the center of the ring is zero.

The electric field at a point on the axis of a uniformly charged ring is given by E = (kλ)/(4πx²), where k is the electrostatic constant, λ is the linear charge density, and x is the distance from the center of the ring.

According to Gauss's law, the electric field inside a uniformly charged spherical shell is zero. This is because the net flux through any closed surface inside the shell is zero, indicating that the electric field is zero.

The electric field at a point perpendicular to the midpoint of a uniformly charged rod is given by E = (kQ)/(4πr), where k is the electrostatic constant, Q is the total charge on the rod, and r is the distance from the midpoint.