Electric Charges and Fields Class 12 Notes

Electric Charge and Its Properties

• $\text{Additive}:$
• the net charge of a system is the algebraic sum of individual charges.
• $\text{Conserved}:$
• charge can be transferred but never created or destroyed (net charge of an isolated system is constant).
• $\text{Quantised}:$
• $q = ne$
• , where
• $n$
• is an integer.
• $\text{Invariant}:$
• charge does not depend on the speed of the charge.

Coulomb's Law

Coulomb's law is valid only for point charges and obeys the principle of superposition: the net force on a charge is the vector sum of the forces from each other charge taken one at a time.

Electric Field and Field Lines

• Field lines start on positive charges and end on negative charges.
• Two field lines never cross each other.
• The tangent to a field line at a point gives the direction of the electric field there.
• The density of lines (closer spacing) indicates a stronger field.
• Field lines are perpendicular to the surface of a conductor.
• In a uniform field the lines are parallel and equally spaced.

Electric Dipole

Axial field (on the axis, far from the dipole): $E_a = \frac{2kp}{r^3}$. Equatorial field: $E_e = \frac{kp}{r^3}$. On an external uniform field $\vec{E}$, the dipole experiences a torque $\vec{\tau} = \vec{p}\times\vec{E}$ but no net force, so it rotates to align with the field.

Electric Flux and Gauss's Law

• $\text{Infinite sheet}:$
• $E = \frac{\sigma}{2\varepsilon_0}$
• , independent of distance.
• $\text{Solid conducting sphere}:$
• $E = 0$
• inside;
• $E = \frac{1}{4\pi\varepsilon_0}\frac{Q}{r^2}$
• outside (r > R).
• $\text{Thin infinite line}:$
• $E = \frac{\lambda}{2\pi\varepsilon_0 r}$
• .

Key Formulas

Solved Examples

Example: Two charges $q_1 = 2\,\mu\text{C}$ and $q_2 = 3\,\mu\text{C}$ are 10 cm apart. Find the magnitude of the force between them.

Solution: Using $F = k\,q_1q_2/r^2$: $F = 9\times10^9 \times \frac{(2\times10^{-6})(3\times10^{-6})}{(0.1)^2} = 5.4\,\text{N}$.