### Concept-Of-Charge-And-Coulombs-Law-By-Prof-K-Thyagarajan

**1. Electric Field ((E)):**

- The electric field at a point in space is a vector quantity that represents the force experienced by a positive test charge placed at that point.

**2. Electric Field Due to a Point Charge ((Q)):**

- The electric field ((E)) due to a point charge (Q) at a distance (r) from the charge is given by Coulomb’s law:
$$[E = \frac{k \cdot |Q|}{r^2}]$$
- (E) is the magnitude of the electric field.
- (k) is Coulomb’s constant $$((k \approx 8.99 \times 10^9 , \text{N}\cdot\text{m}^2/\text{C}^2)).$$
- (Q) is the magnitude of the point charge.
- (r) is the distance from the charge to the point of interest.

**3. Superposition Principle:**

- The total electric field at a point due to multiple point charges is the vector sum of the electric fields produced by each charge individually.

**4. Electric Field Due to a Uniformly Charged Infinite Plane:**

- For an infinite uniformly charged plane with surface charge density σ, the electric field above the plane is given by:
$$[E = \frac{\sigma}{2\epsilon_0}]$$
- σ is the surface charge density.
- ε
_{0}is the permittivity of free space $$((\epsilon_0 \approx 8.85 \times 10^{-12} , \text{C}^2/\text{N}\cdot\text{m}^2)).$$

**5. Electric Field Due to a Uniformly Charged Line:**

- For a uniformly charged line with linear charge density λ, the electric field at a distance (r) from the line is given by:
$$[E = \frac{2k\lambda}{r}]$$
- λ is the linear charge density.

**6. Electric Field Due to a Uniformly Charged Ring:**

- For a uniformly charged ring with total charge (Q) and radius (R), the electric field on its axis at a distance (x) from the center of the ring is given by: $$[E = \frac{kQx}{(x^2 + R^2)^{3/2}}]$$

**7. Electric Field Due to a Uniformly Charged Disk:**

- For a uniformly charged disk with surface charge density (\sigma), the electric field on its axis at a distance (z) from the center of the disk is given by: $$[E = \frac{\sigma}{2\epsilon_0}\left(1 - \frac{z}{\sqrt{z^2 + R^2}}\right)]$$

**8. Electric Field Lines:**

- Electric field lines are imaginary lines that represent the direction and intensity of an electric field.
- Electric field lines originate from positive charges and terminate on negative charges.
- They never cross each other, and the density of field lines indicates the strength of the field.

###### 1. Electric Charge

Electric charge is a fundamental property of matter. It can be positive or negative. The unit of charge is the Coulomb (C). The charge of an electron is approximately -1.602 x 10^-19 C, and that of a proton is +1.602 x 10^-19 C.

###### 2. Coulomb’s Law

Coulomb’s law describes the electrostatic force between two point charges. The law states that the force (F) between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance (r) between them. Mathematically, Coulomb’s law is expressed as: $$F = \frac{k * |q1 * q2|}{r^2}$$

##### Where:

- F is the electrostatic force between the charges.
- q1 and q2 are the magnitudes of the charges.
- r is the distance between the charges.
- k is Coulomb’s constant, approximately equal to 8.988 x 10^9 N m^2/C^2.

###### 3. Direction of the Force

The force between charges is attractive if the charges are of opposite sign (one positive and one negative) and repulsive if the charges have the same sign (both positive or both negative).

###### 4. Superposition Principle

Coulomb’s law obeys the superposition principle, which means that the net force on a charge due to multiple other charges is the vector sum of the forces due to each individual charge.

###### 5. Electric Field (E)

- Electric field is a property of space around a charged object.
- It is defined as the force per unit positive charge at a point in space.
- Electric field (E) at a point is given by: $$E = \frac{F}{q}$$ Where F is the force on a test charge (q) placed at that point.

###### 6. Electric Field Due to a Point Charge

The electric field (E) due to a point charge (Q) at a distance (r) from it is given by: $$E = \frac{k * |Q|}{r^2}$$

###### 7. Electric Field Due to Multiple Charges

To find the electric field at a point due to multiple charges, you can calculate the electric field produced by each charge individually and then vectorially sum them up.

###### 8. Electric Potential (Voltage)

Electric potential (V) at a point in an electric field is the work done per unit positive charge in bringing a test charge from infinity to that point. The electric potential at a point in an electric field is given by: $$V = \frac{k * Q}{r}$$