Chapter 1: Electric Charges & Fields
Vol 1: Electric Charge & Coulomb's Law
Electric Charge: Intrinsic property of matter responsible for electric and magnetic effects.
• Quantization: $Q = \pm ne$ (where $e = 1.6 \times 10^{-19}$ C).
• Conservation: Total charge of an isolated system remains constant.
Coulomb's Law
The force between two point charges is directly proportional to the product of charges and inversely proportional to the square of the distance between them.
[attachment_0](attachment)$k = \frac{1}{4\pi\epsilon_0} \approx 9 \times 10^9 \text{ Nm}^2/\text{C}^2$
Superposition Principle: Force on a charge due to multiple charges is the vector sum of individual forces.
$\vec{F}_{net} = \vec{F}_1 + \vec{F}_2 + \dots$
Vol 2: Electric Field & Dipole
Electric Field ($\vec{E}$): Force experienced by a unit positive test charge. ($\vec{E} = \vec{F}/q_0$).
[attachment_1](attachment)Electric Dipole
A system of two equal and opposite charges separated by a small distance $2a$.
Dipole Moment: $\vec{p} = q \times 2a$ (Directed from -q to +q).
$$\vec{E}_{axial} = \frac{1}{4\pi\epsilon_0} \frac{2\vec{p}}{r^3}$$
$$\vec{E}_{eq} = - \frac{1}{4\pi\epsilon_0} \frac{\vec{p}}{r^3}$$
Note: $E_{axial} = 2 E_{eq}$ for short dipoles.
Dipole in Uniform Field
Torque ($\tau$): $\vec{\tau} = \vec{p} \times \vec{E} = pE \sin \theta$.
Vol 3: Electric Flux & Gauss's Law
Electric Flux ($\Phi_E$): Total number of field lines passing normally through a surface.
$\Phi_E = \oint \vec{E} \cdot d\vec{A} = EA \cos \theta$.
Gauss's Law
The total electric flux through a closed surface is $1/\epsilon_0$ times the net charge enclosed by the surface.
$$\Phi_E = \oint \vec{E} \cdot d\vec{A} = \frac{q_{in}}{\epsilon_0}$$Applications of Gauss's Law
| Charge Distribution | Formula for E |
|---|---|
| Infinitely Long Wire ($\lambda$) | $$E = \frac{\lambda}{2\pi\epsilon_0 r}$$ |
| Infinite Plane Sheet ($\sigma$) | $$E = \frac{\sigma}{2\epsilon_0}$$ (Independent of distance) |
| Thin Spherical Shell ($q$) |
• Outside ($r>R$): $E = k q / r^2$ • Inside ($r |
Vol 4: Mission 100 Question Bank
Section A: MCQs
Q1. The electric flux through a closed surface enclosing an electric dipole is:
(a) $q/\epsilon_0$ (b) $2q/\epsilon_0$ (c) Zero (d) Infinite
Ans: (c) Zero (Net charge of dipole = +q - q = 0).
Q2. Which physical quantity has the unit N/C?
(a) Electric Flux (b) Electric Field (c) Potential (d) Charge
Ans: (b) Electric Field.
Section B: Numericals (Important)
Q3. A polythene piece rubbed with wool is found to have a negative charge of $3 \times 10^{-7}$ C. Estimate the number of electrons transferred.
Solution:
Given: $Q = 3 \times 10^{-7}$ C, $e = 1.6 \times 10^{-19}$ C.
Formula: $Q = ne \Rightarrow n = Q/e$
$n = \frac{3 \times 10^{-7}}{1.6 \times 10^{-19}} = 1.875 \times 10^{12}$ electrons.
Ans: $1.875 \times 10^{12}$ electrons (from wool to polythene).
Section C: Conceptual
Q4. Why can't two electric field lines cross each other?
Ans: If they intersect at a point, there would be two tangents at that point, implying two directions of the electric field at the same location, which is physically impossible.
Mission 100 Physics Series
Next Chapter: Electrostatic Potential & Capacitance
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