Electric Charges (Concise Notes)
- Defintion
- Fundamental property of matter
- Experience a force in electromagnetic field
- Cause of electromagnetic field/force
- RUDD
- Representation – Q,q
- Unit – Coulomb (C), mC, (micro C)
- Dimension – [AT}
- Vector
- Charge distribution
- Discrete charges – localized
- Continuous (uniform) charge distribution
- Linear charge distribution, \(\lambda\), \(Cm^{-1}\)
- Surface charge distribution, \(\sigma\), \(Cm^{-2}\)
- Volume charge distribution, \(\rho\), \(Cm^{-3}\)
- Prerequisite
- Point Charge –
- an idealized model of a particle
- treated as if all the charge is concentrated at a single point in space
- actual size of the charged object is much smaller compared to the distances involved
- Newton’s law of Gravitation
- \(F_g= G \frac{m_1m_2}{r^2}\)
- Vector
- unit vector, \(\hat r = \frac {\overrightarrow r}{r}\)
- Point Charge –
- Derivation
- dependency on charges, \(F \propto \ q_1q_2\)
- dependency on distance between two, \(F \propto \frac{1}{r^2}\)
- the constant term for free space- variation with medium, \(k = \frac{1}{4 \pi \epsilon_0}\)
- meaning of sign of the force, positive force \(\implies\) repulsive force, negative force \(\implies\) attractive force
- Statement, \(F = k \frac{q_1q_2}{r^2}\)
- Vector form of Coulomb’s Law
- in terms of unit vector and displacement vector
- \(\overrightarrow{F_{BA}} = k\frac{q_1 q_2}{|AB|^2} \overrightarrow{AB}\)
- \(\overrightarrow{F_{BA}} = k\frac{q_1 q_2}{|AB|^2} \overrightarrow{AB}\)
- Validity of Newton’s 3rd law of motion
- in terms of unit vector and displacement vector
- Definition of one Coulomb charge
- An amount of charge which experience an electric force of \(9 \times 10^9 N\) from an identical charge placed at a distance of 1m
| Point of comparison | Electric force vs Gravitational Force |
|---|---|
| Strength | \(\frac{F_e}{F_g} ≈ 10^{39}\) between electron and proton of hydrogen atom |
| Nature of Force | \(F_e\) – attractive as well repulsive \(F_g\) – only attractive |
| Source of Force | \(F_e\) – electric charges \(F_g\) – masses |
- Prerequisite
- Addition of vectors
- Coulomb’s Law
- Superposition principle of coulomb’s force
- Net force on any charge = vector sum of individual forces experienced by the charge from other charges
- \(\overrightarrow{F_{D}} = \overrightarrow{F_{DA}} +\overrightarrow{F_{DB}} +\overrightarrow{F_{DC}} \)
