Notes from the JEE Toppers
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 qt 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, $$(E_{\text{net}} = E_1 + E_2 + E_3 + \ldots),$$ where $$(E_{\text{net}})$$ is the net electric field and $$(E_1, E_2, E_3, \ldots)$$ 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.