Electric Charges and Fields

Study Notes

Gauss's Law states that the total electric flux through a closed surface is proportional to the charge enclosed within the surface.
Mathematically, it is represented as: Φ = ∫∫E·dA = q/ε₀
Where:
- Φ is the total electric flux
- E is the electric field
- dA is the area element
- q is the total charge enclosed
- ε₀ is the electric constant (permittivity of free space)
Gauss's Law is useful for calculating the electric field of a symmetric distribution of charges.

An electric dipole is a pair of equal and opposite charges separated by a small distance.
The electric dipole moment (p) is a vector that characterizes the dipole, with magnitude p = qd, where d is the distance between the charges.
The electric field of a dipole decreases with distance as 1/r³, whereas the electric field of a single charge decreases as 1/r².
Electric dipoles are important in understanding the behavior of molecules and their interactions with electric fields.

Electric field lines are imaginary lines that emerge from positive charges and enter into negative charges.
The direction of the electric field lines at a point is the direction of the electric field at that point.
Electric field lines are continuous and do not intersect with each other.
The density of electric field lines represents the strength of the electric field.
Electric field lines can be used to visualize and understand the electric field around a distribution of charges.

Coulomb's Law states that the electric force (F) between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
Mathematically, it is represented as: F = k * (q₁ * q₂) / r²
Where:
- F is the electric force
- k is Coulomb's constant
- q₁ and q₂ are the two point charges
- r is the distance between the charges
Coulomb's Law is used to calculate the electric force between two point charges.
It is a fundamental principle in understanding the interactions between charged objects.