“Field is a vector, potential is a number”
Adding contributions from several charges
Add fields with directions and components. Add potentials as plain numbers with their signs. Most electrostatics errors are adding fields like numbers.
Class 12 Physics · Gujarat Board, CBSE, GUJCET, JEE and NEET
Electrostatics formulas
Electrostatics opens Class 12 and sets the pattern for the whole year: a field, a potential, and an energy, for each of which there is one formula and one sign rule. Gauss's law here is the shortcut that turns page-long integrals into single lines.
17 formulas, 4 memory hooks, and the 5 mistakes that cost the most marks.
Force and field
| What | Formula | Symbols and notes |
|---|---|---|
| Coulomb's law | F = kq₁q₂/r² | k = 1/4πε₀ = 9 × 10⁹ N m² C−2 |
| In a medium | Fmedium = Fvacuum/K | K is the dielectric constant of the medium |
| Electric field | E = F/q = kQ/r² | unit N C−1 or V m−1 |
| Field of a dipole, axial | E = 2kp/r³ | along the dipole axis, for r much greater than the dipole length |
| Field of a dipole, equatorial | E = kp/r³ | half the axial value, and opposite in direction |
| Dipole moment | p = q × 2a | directed from the negative charge to the positive |
| Torque on a dipole | τ = pE sinθ | zero when the dipole lines up with the field |
Gauss's law
| What | Formula | Symbols and notes |
|---|---|---|
| Gauss's law | Φ = qenclosed/ε₀ | the flux depends only on the charge inside |
| Infinite line charge | E = λ/2πε₀r | λ is charge per unit length; E falls as 1/r |
| Infinite sheet of charge | E = σ/2ε₀ | independent of distance from the sheet |
| Charged conducting shell, outside | E = kQ/r² | behaves as if all the charge were at the centre |
| Charged conducting shell, inside | E = 0 | which is why a car is safe in a lightning strike |
Potential and energy
| What | Formula | Symbols and notes |
|---|---|---|
| Potential of a point charge | V = kQ/r | a scalar, so potentials simply add |
| Relation to field | E = −dV/dr | the field points from high potential to low |
| Potential energy of two charges | U = kq₁q₂/r | negative for unlike charges |
| Work done | W = q(VB − VA) | independent of the path taken |
| Dipole potential energy | U = −pE cosθ | minimum when aligned with the field |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Axial is twice equatorial”
Dipole fields
Along the axis 2kp/r³, on the perpendicular bisector kp/r³, and the two point opposite ways.
“Inside a conductor, nothing”
Fields in conductors and shells
The field inside the material of a conductor and inside a hollow charged shell is zero, and all the charge sits on the outer surface.
“Cube of r for dipoles”
How dipole fields fall off
A single charge falls as 1/r², a dipole as 1/r³, because its two opposite charges nearly cancel at a distance.
Where marks go
The mistakes that cost the most.
- Adding electric fields as if they were scalars. They are vectors and need components.
- Forgetting that the field inside a charged conducting shell is zero while the potential inside is not; the potential is constant and equal to the surface value.
- Using 1/r² for a dipole field. It falls as 1/r³.
- Dropping the sign of the charge in potential and potential energy, which flips the answer.
- Thinking Gauss's law only works for a sphere. It always holds; it is only useful when the symmetry is high.
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