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Electric Charges and Fields - Handwritten Notes for Physics JEE & NEET

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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=kr2q1​q2​​, 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=4πϵ0​1​r32p​.

  • Along the equatorial line, E=14πϵ0pr3E = \frac{1}{4 \pi \epsilon_0} \frac{p}{r^3}E=4πϵ0​1​r3p​.

Gauss's Law:

  • The total electric flux through a closed surface is equal to 1ϵ0\frac{1}{\epsilon_0}ϵ0​1​ 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=ϵ0​Qenc​​.

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=dϵ0​A​, 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.

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