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TRANSCRIPT OF NOTES:
Electric Charge:
Matter contains electric force.
Electric charges exert forces on each other.
Law of Conservation of Charge:
Charge is neither created nor destroyed but is transferred from one body to another.
The total charge in an isolated system remains constant.
Quantization of Charge:
Charge exists in discrete packets called quanta.
The smallest charge is the charge on an electron.
Charge is always a multiple of the fundamental charge e=1.6×10−19 Ce = 1.6 \times 10^{-19} \, \text{C}e=1.6×10−19C.
Coulomb's Law:
The force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Mathematically: F=kq1q2r2F = k \frac{q_1 q_2}{r^2}F=kr2q1q2, where kkk is Coulomb's constant (k≈8.99×109 N m2/C2k \approx 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2k≈8.99×109N m2/C2).
Electric Field:
The region around a charged particle where its force is exerted on other charges.
Electric field EEE at a point is defined as E=FqE = \frac{F}{q}E=qF.
The direction of the field is the direction of the force on a positive test charge.
Electric Dipole:
Consists of two equal and opposite charges separated by a small distance.
The electric dipole moment ppp is given by p=q⋅dp = q \cdot dp=q⋅d, where ddd is the distance between charges.
Electric Field of a Dipole:
Along the axial line of the dipole, the electric field EEE at distance rrr is E=14πϵ02pr3E = \frac{1}{4 \pi \epsilon_0} \frac{2p}{r^3}E=4πϵ01r32p.
Along the equatorial line, E=14πϵ0pr3E = \frac{1}{4 \pi \epsilon_0} \frac{p}{r^3}E=4πϵ01r3p.
Gauss's Law:
The total electric flux through a closed surface is equal to 1ϵ0\frac{1}{\epsilon_0}ϵ01 times the charge enclosed by the surface.
Mathematically: ΦE=∮E⋅dA=Qencϵ0\Phi_E = \oint E \cdot dA = \frac{Q_{\text{enc}}}{\epsilon_0}ΦE=∮E⋅dA=ϵ0Qenc.
Potential Energy in an Electric Field:
The work done to move a charge qqq in an electric field EEE is given by W=qEdW = qEdW=qEd.
Electric potential VVV at a point is defined as the work done per unit charge to move a test charge from infinity to that point: V=WqV = \frac{W}{q}V=qW.
Conductors and Insulators:
Conductors allow free movement of electric charge, while insulators do not.
In a conductor, electric field inside is zero in electrostatic equilibrium.
The charge resides on the surface of the conductor.
Electric Flux:
The measure of the number of electric field lines passing through a given area.
Mathematically: ΦE=E⋅A⋅cos(θ)\Phi_E = E \cdot A \cdot \cos(\theta)ΦE=E⋅A⋅cos(θ).
Capacitance:
The ability of a system to store charge per unit potential difference.
Mathematically: C=QVC = \frac{Q}{V}C=VQ, where CCC is the capacitance, QQQ is the charge, and VVV is the potential difference.
For a parallel plate capacitor, C=ϵ0AdC = \frac{\epsilon_0 A}{d}C=dϵ0A, where AAA is the area of the plates and ddd is the separation between them.
Example Problems:
1. Transfer of Charge Between Two Point Charges:
Two point charges AAA and BBB with charges +Q+Q+Q and −Q-Q−Q are placed a distance apart with force FFF between them.
If 25% of the charge from AAA is transferred to BBB, the new force between the charges can be calculated using Coulomb's law with the modified charges.
2. Force Between Two Ions:
Two positive ions, each with charge qqq, are separated by distance ddd. The force FFF of repulsion between them can be determined using Coulomb's law.
The number of electrons missing from each ion can be calculated by equating q=n⋅eq = n \cdot eq=n⋅e.
3. Electric Field Between Parallel Line Charges:
Two parallel infinite line charges with linear charge densities +λ+\lambda+λ and −λ-\lambda−λ are placed at a distance 2R2R2R apart.
The electric field midway between the two line charges is determined by superimposing the electric fields due to each line charge.
These notes provide a concise overview of key concepts in electrostatics, including fundamental laws, principles, and example problems. For further details and handwritten notes, visit crookshanksacademy.com/jeeneet.