Electrostatics

Concept: Gauss’s theorem helps calculate electric fields for highly symmetric charge distributions such as spherical, cylindrical, or planar symmetry. Statement of Gauss’s Theorem: The total electric flux through a closed surface is equal to times the total charge enclosed within the surface. where:
= electric field
= area vector
= permittivity of free space
Electric field due to an infinitely long straight charged wire Let:
Linear charge density = (charge per unit length)
Distance from wire =
Step 1: Choose Gaussian surface Due to cylindrical symmetry, choose a cylindrical Gaussian surface:
Radius =
Length =
The electric field is:
Radial
Same magnitude everywhere on curved surface
Step 2: Calculate electric flux Flux through cylinder:
Curved surface contributes flux
Flat ends give zero flux (field parallel to surface)
Step 3: Charge enclosed Step 4: Apply Gauss’s Law Cancel : Final Result:
Field decreases inversely with distance.
Field is radially outward for positive charge.

Concept: According to Coulomb's Law, the electrostatic force between two point charges is: where:
= force between charges
= distance between charges
Thus, force is inversely proportional to the square of the distance. Step 1: Original force Step 2: If distance is doubled New distance = Step 3: Compare forces So, the force becomes one-fourth of the original value.