1. Electric Field (E)

The electric field is a vector quantity that describes the force experienced by a positive test charge placed at a given point in space due to the presence of other charges.

2. Electric Field at a Point

The electric field ((E)) at a point in space is defined as the force ((F)) experienced by a positive test charge q_t placed at that point, divided by the magnitude of the test charge: $$(E=\frac{F}{q_t}).$$

3. Direction of Electric Field

• The electric field points in the direction of the force that a positive test charge would experience when placed at that point.
• For positive charges, the electric field points away from the charge.
• For negative charges, the electric field points toward the charge.

4. Electric Field Due to Point Charges

The electric field ((E)) at a point due to a point charge ((Q)) is given by Coulomb’s law: $$(E=\frac{k|Q|}{r^2}),$$ where (k) is Coulomb’s constant and (r) is the distance from the charge.

5. Superposition Principle

The total electric field at a point due to multiple charges is the vector sum of the electric fields produced by each individual charge. Mathematically, $$(E_{\text{net}}=E_1+E_2+E_3+\dots ),$$ where $$(E_{\text{net}})$$ is the net electric field and $$(E_1,E_2,E_3,\dots )$$ are the electric fields due to individual charges.

6. Electric Field Lines

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

7. Electric Field Inside and Outside Conductors

• Inside a conductor in electrostatic equilibrium, the electric field is zero.
• On the surface of a conductor in electrostatic equilibrium, the electric field is perpendicular to the surface.

8. Electric Field Due to Continuous Charge Distributions

To find the electric field due to a continuous charge distribution, integrate the contributions from infinitesimally small charge elements using the appropriate formula.