Key Concepts to Remember for JEE and CBSE Board Exams on Charge and Coulomb’s Law

Electric Charge

• Charge quantization: Electric charges always occur in discrete multiples of the elementary charge (e), where (e = 1.602\times10^{-19} C).

• Conductors and insulators: Conductors allow electric charges to move freely within them, while insulators do not.

Coulomb’s Law

• Statement: Coulomb’s Law states that the magnitude of the electrostatic force between two point charges (q_1) and (q_2) separated by a distance (r) is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

• Mathematical expression: $$F = k \frac{|\ q_1 \ q_2| }{r^2} $$ where (k) is the electrostatic constant ( (k = 8.988 \times 10^9 N\cdot m^2/C^2) )

• Force between point charges: The force between two point charges is attractive if the charges have opposite signs and repulsive if they have the same sign.

• Superposition principle: If there are multiple charges present, the total force acting on any one charge is the vector sum of the forces exerted by all other charges.

Electric Field

• Definition: The electric field at a point is a vector quantity that describes the strength and direction of the electric force that would be experienced by a positive test charge placed at that point.

• Electric field due to a point charge: The electric field due to a point charge (q) at a distance (r) is given by $$ \vec{E} = k\frac{q}{r^2} \hat{r} $$ where (\hat{r}) is the unit vector pointing away from the charge.

• Electric field lines: Electric field lines are imaginary lines drawn in such a way that their direction at each point is tangent to the electric field vector at that point. The density of the field lines indicates the strength of the electric field.

Electric Potential

• Definition: Electric potential at a point is the amount of electric potential energy per unit positive charge at that point.

• Potential due to a point charge: The electric potential due to a point charge (q) at a distance (r) is given by $$ V = k\frac{q}{r} $$

Gauss’s Law

• Statement: Gauss’s Law states that the net flux of the electric field through any closed surface is equal to the total charge enclosed by that surface divided by the permittivity of free space (\epsilon_0)

• Mathematical expression: $$\oint \overrightarrow{E} \cdot \hat{n} dA = \frac{Q_{enc}}{\epsilon_0}$$

where (\overrightarrow{E}) is the electric field, (\hat{n}) is a unit vector perpendicular to the surface, (dA) is the differential of area, (Q_{enc}) is the total charge enclosed by the surface, and (\epsilon_0 = 8.85\times 10^{-12} C^2/Nm^2) is the permittivity of free space.

• Application: Gauss’s Law can be used to calculate the electric field in certain symmetric charge distributions without having to consider individual charges.