Electrostatics — Revision Notes

⚡ 30-Second Revision

Charge: — Quantized ($q = pm ne$), Conserved. SI unit: Coulomb (C).
Coulomb's Law: — $F = k \frac{|q_1 q_2|}{r^2}$, $k = 9 \times 10^9,\text{N m}^2/\text{C}^2$.
Electric Field (Point Charge): — $E = k \frac{Q}{r^2}$. Vector quantity. Direction away from +Q, towards -Q.
Electric Potential (Point Charge): — $V = k \frac{Q}{r}$. Scalar quantity.
Electric Dipole Moment: — $vec{p} = q(2vec{a})$. Direction from $-q$ to $+q$.
Torque on Dipole: — $vec{\tau} = vec{p} \times vec{E}$, $au = pE sin\theta$.
Potential Energy of Dipole: — $U = -vec{p} cdot vec{E} = -pE cos\theta$.
Electric Flux: — $Phi_E = int vec{E} cdot dvec{A}$.
Gauss's Law: — $oint vec{E} cdot dvec{A} = \frac{Q_{enclosed}}{epsilon_0}$.
Relation E and V: — $vec{E} = -

abla V$, or$E_x = -rac{dV}{dx}$.

Potential Energy (System of 2 charges): — $U = k \frac{q_1 q_2}{r}$.
Conductor Properties: — $E_{inside}=0$, $V_{inside}=\text{constant}$, charge on surface, field lines $perp$ surface.

2-Minute Revision

Electrostatics is the study of stationary charges. Key concepts begin with electric charge, which is quantized and conserved. Coulomb's Law dictates the force between two point charges, varying inversely with the square of their separation.

This force creates an electric field around charges, which is a vector quantity, while electric potential is a scalar measure of potential energy per unit charge. The relationship $E = -dV/dr$ is crucial, showing that the field points in the direction of decreasing potential.

Gauss's Law offers a powerful method to calculate electric fields for symmetric charge distributions by relating total flux through a closed surface to the enclosed charge. Electric dipoles, consisting of two equal and opposite charges, experience torque and possess potential energy in an external electric field.

Remember that inside a conductor, the electric field is zero, and the potential is constant, equal to that on its surface. Equipotential surfaces are always perpendicular to electric field lines. Focus on understanding the vector nature of force and field versus the scalar nature of potential and energy, as this is a common area for conceptual errors.

5-Minute Revision

Begin your revision by solidifying the fundamental definitions: electric charge (quantization, conservation, additivity), Coulomb's Law ($F = k \frac{|q_1 q_2|}{r^2}$), and the principle of superposition for multiple charges.

Understand the concept of electric field ($vec{E} = vec{F}/q_0$) as a vector quantity and how to calculate it for point charges and simple continuous distributions. Visualize electric field lines and their properties (origin from positive, end on negative, never cross, density indicates strength).

Next, move to electric potential ($V = W/q_0$), a scalar quantity, and electric potential energy ($U = qV$ or $U = k \frac{q_1 q_2}{r}$). Grasp the crucial relationship between electric field and potential, $vec{E} = - abla V$, and its implications (field points towards decreasing potential, equipotential surfaces are perpendicular to field lines).

Practice calculating potential and potential energy for systems of charges. Gauss's Law ($oint vec{E} cdot dvec{A} = \frac{Q_{enclosed}}{epsilon_0}$) is a powerful tool for symmetric charge distributions; know its applications for infinite line, plane sheet, and spherical shells/solids.

Finally, revise electric dipoles: their dipole moment ($vec{p} = q(2vec{a})$), the torque they experience in a uniform field ($vec{\tau} = vec{p} \times vec{E}$), and their potential energy ($U = -vec{p} cdot vec{E}$).

Don't forget the unique properties of conductors in electrostatic equilibrium: zero electric field inside, constant potential throughout, and charge residing on the surface. Work through a few quick examples for each concept to ensure clarity.

For instance, calculate the potential at the center of a square with charges at corners, or the field inside a uniformly charged non-conducting sphere.

Prelims Revision Notes

1
Electric Charge: — Fundamental property. Quantized ($q = pm ne$, $e = 1.6 \times 10^{-19},\text{C}$). Conserved. Scalar. Like charges repel, unlike attract.
2
Coulomb's Law: — Force between two point charges $q_1, q_2$ separated by $r$: $F = k \frac{|q_1 q_2|}{r^2}$. $k = \frac{1}{4piepsilon_0} = 9 \times 10^9,\text{N m}^2/\text{C}^2$. In a medium, $F_m = F_{vacuum}/K$.
3
Electric Field ($vec{E}$): — Force per unit positive test charge. $vec{E} = vec{F}/q_0$. Unit: N/C or V/m. For point charge $Q$: $E = k \frac{Q}{r^2}$. Vector sum for multiple charges.
4
Electric Field Lines: — Originate from +ve, terminate on -ve. Never cross. Tangent gives direction. Density indicates strength. Perpendicular to conductor surfaces.
5
Electric Potential ($V$): — Work done per unit positive test charge from infinity. $V = W/q_0$. Unit: Volt (V) or J/C. For point charge $Q$: $V = k \frac{Q}{r}$. Scalar sum for multiple charges.
6
Electric Potential Energy ($U$): — Energy of a charge $q$ in potential $V$: $U = qV$. For two charges $q_1, q_2$: $U = k \frac{q_1 q_2}{r}$. For system, sum of all pairs.
7
Relation between E and V: — $vec{E} = -

abla V$. In 1D,$E_x = -dV/dx$. Field points in direction of decreasing potential.

1
Equipotential Surfaces: — Constant potential. No work done moving charge. Perpendicular to $vec{E}$ lines.
2
Electric Dipole: — Charges $+q, -q$ separated by $2a$. Dipole moment $vec{p} = q(2vec{a})$ (from $-q$ to $+q$).

* Axial field: $E_{axial} = k \frac{2p}{r^3}$. Axial potential: $V_{axial} = k \frac{p}{r^2}$. * Equatorial field: $E_{equatorial} = k \frac{p}{r^3}$ (opposite to $vec{p}$). Equatorial potential: $V_{equatorial} = 0$. * Torque in uniform $vec{E}$: $vec{\tau} = vec{p} \times vec{E}$, $au = pE sin\theta$. * Potential Energy in uniform $vec{E}$: $U = -vec{p} cdot vec{E} = -pE cos\theta$.

1
Electric Flux ($Phi_E$): — $Phi_E = int vec{E} cdot dvec{A}$.
2
Gauss's Law: — $oint vec{E} cdot dvec{A} = \frac{Q_{enclosed}}{epsilon_0}$.

* Infinite line: $E = \frac{lambda}{2piepsilon_0 r}$. * Infinite plane sheet: $E = \frac{sigma}{2epsilon_0}$. * Charged spherical shell (or conductor): $E_{out} = k \frac{Q}{r^2}$, $E_{in} = 0$. $V_{out} = k \frac{Q}{r}$, $V_{in} = k \frac{Q}{R}$. * Solid non-conducting sphere: $E_{out} = k \frac{Q}{r^2}$, $E_{in} = k \frac{Qr}{R^3}$.

1
Conductors in Electrostatic Equilibrium: — $E_{inside}=0$. Net charge resides on surface. Potential is constant throughout volume. Field lines perpendicular to surface.

Vyyuha Quick Recall

Charges Exert Powerful Forces, Varying Gradually. (Charges, Electric field, Potential, Force, Varying potential, Gauss's Law). Or, for the relationship between E and V: Electric Field Decreases Voltage (E is negative derivative of V).