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Elecrostatics formulas

Master Elecrostatics through 34 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Elecrostatics, every formula

34 formulas, typeset and free. Print it, or keep it open beside your practice.

Coulomb's force
$F = \frac{1}{4 π ε _{0}} \frac{q _{1} q _{2}}{r ^{2}}$
Q1MCQCoulomb's force
The force between two charges varies as:
- A
  $\dfrac{1}{r^{2}}$
- B
  $r^{2}$
- C
  $\dfrac{1}{r}$
- D
  $r$
Coulomb constant
$k = \frac{1}{4 π ε _{0}} = 9 \times 1 0^{9} N m^{2} C^{- 2}$
Q1MCQCoulomb constant
The value of $\dfrac{1}{4\pi\varepsilon_0}$ is:
- A
  $9\times10^{9}$
- B
  $8.85\times10^{-12}$
- C
  $6.67\times10^{-11}$
- D
  $3\times10^{8}$
Electric field
$E = \frac{F}{q} = \frac{k Q}{r ^{2}} \overset{r}{^}$
Q1MCQElectric field
The field of a point charge is:
- A
  $\dfrac{kQ}{r^{2}}$
- B
  $\dfrac{kQ}{r}$
- C
  $kQr$
- D
  $\dfrac{kQ}{r^{3}}$
Force on a charge
$F = q E$
Field of a line charge
$E = \frac{λ}{2 π ε _{0} r} = \frac{2 k λ}{r}$
Q1MCQLine charge field
The field of an infinite line charge is:
- A
  $\dfrac{2k\lambda}{r}$
- B
  $\dfrac{k\lambda}{r^{2}}$
- C
  $\dfrac{\lambda}{\varepsilon_0}$
- D
  $\dfrac{k\lambda}{r}$
Field of a nonconducting sheet
$E = \frac{σ}{2 ε _{0}}$
Q1MCQNonconducting sheet
The field of an infinite nonconducting sheet is:
- A
  $\dfrac{\sigma}{2\varepsilon_0}$
- B
  $\dfrac{\sigma}{\varepsilon_0}$
- C
  $\dfrac{\sigma}{4\varepsilon_0}$
- D
  $2\sigma\varepsilon_0$
Field of a conducting sheet
$E = \frac{σ}{ε _{0}}$
Q1MCQConducting sheet
The field just outside a charged conducting surface is:
- A
  $\dfrac{\sigma}{\varepsilon_0}$
- B
  $\dfrac{\sigma}{2\varepsilon_0}$
- C
  $0$
- D
  $\dfrac{\sigma}{4\varepsilon_0}$
Field on the axis of a ring
$E = \frac{k Q x}{( R ^{2} + x ^{2} ) ^{3/2}}$
Q1MCQRing axis
The field on the axis of a charged ring is:
- A
  $\dfrac{kQx}{(R^{2}+x^{2})^{3/2}}$
- B
  $\dfrac{kQ}{x^{2}}$
- C
  $\dfrac{kQ}{R^{2}}$
- D
  $0$
Field at the centre of a ring
$E = 0$
Field of a shell (outside/inside)
$E = \frac{k Q}{r ^{2}} (r > R), E = 0 (r < R)$
Q1MCQShell field
The field inside a charged conducting shell is:
- A
  $0$
- B
  $\dfrac{kQ}{r^{2}}$
- C
  $\dfrac{kQ}{R^{2}}$
- D
  $\dfrac{kQ}{R}$
Field inside a solid sphere
$E = \frac{k Q r}{R ^{3}} (r < R)$
Q1MCQSolid sphere inside
Inside a uniformly charged solid sphere, the field is:
- A
  $\dfrac{kQr}{R^{3}}$
- B
  $\dfrac{kQ}{r^{2}}$
- C
  $0$
- D
  $\dfrac{kQ}{R^{2}}$
Field of a dipole (axial)
$E = \frac{2 k p}{r ^{3}}$
Q1MCQDipole axial
The field on the axis of a dipole is:
- A
  $\dfrac{2kp}{r^{3}}$
- B
  $\dfrac{kp}{r^{3}}$
- C
  $\dfrac{kp}{r^{2}}$
- D
  $\dfrac{2kp}{r^{2}}$
Field of a dipole (equatorial)
$E = \frac{k p}{r ^{3}}$
Q1MCQDipole equatorial
The field at the equatorial position of a dipole is:
- A
  $\dfrac{kp}{r^{3}}$
- B
  $\dfrac{2kp}{r^{3}}$
- C
  $\dfrac{kp}{r^{2}}$
- D
  $0$
Field of a dipole (general point)
$E = \frac{k p}{r ^{3}} 1 + 3 cos^{2} θ$
Q1MCQDipole general
The field of a dipole at a general point is:
- A
  $\dfrac{kp}{r^{3}}\sqrt{1+3\cos^{2}\theta}$
- B
  $\dfrac{kp}{r^{3}}$
- C
  $\dfrac{2kp}{r^{3}}$
- D
  $\dfrac{kp\cos\theta}{r^{2}}$
Electric potential
$V = \frac{k Q}{r}$
Q1MCQPotential
The potential of a point charge is:
- A
  $\dfrac{kQ}{r}$
- B
  $\dfrac{kQ}{r^{2}}$
- C
  $kQr$
- D
  $\dfrac{kQ}{r^{3}}$
Potential of a dipole
$V = \frac{k p cos θ}{r ^{2}}$
Q1MCQDipole potential
The potential of a dipole is:
- A
  $\dfrac{kp\cos\theta}{r^{2}}$
- B
  $\dfrac{kp}{r}$
- C
  $\dfrac{kp}{r^{3}}$
- D
  $\dfrac{2kp}{r^{2}}$
Potential of a shell
$V = \frac{k Q}{r} (r > R), V = \frac{k Q}{R} (r < R)$
Q1MCQShell potential
The potential inside a charged shell is:
- A
  $\dfrac{kQ}{R}$ (constant)
- B
  $0$
- C
  $\dfrac{kQ}{r}$
- D
  $\dfrac{kQ}{r^{2}}$
Field from potential
$E = - \frac{d V}{d r} = - \nabla V$
Q1MCQE from V
The field relates to potential by:
- A
  $E=-\dfrac{dV}{dr}$
- B
  $E=\dfrac{dV}{dr}$
- C
  $E=Vr$
- D
  $E=-V$
Electric flux
$ϕ = E \cdot A = E A cos θ$
Gauss's law
$ϕ = \oint E \cdot d A = \frac{q _{in}}{ε _{0}}$
Q1MCQGauss's law
The flux through a closed surface enclosing charge $q$ is:
- A
  $\dfrac{q}{\varepsilon_0}$
- B
  $q\varepsilon_0$
- C
  $\dfrac{\varepsilon_0}{q}$
- D
  $0$
PE of two charges
$U = \frac{k q _{1} q _{2}}{r}$
Q1MCQPE of charges
The potential energy of two charges is:
- A
  $\dfrac{kq_1 q_2}{r}$
- B
  $\dfrac{kq_1 q_2}{r^{2}}$
- C
  $kq_1 q_2 r$
- D
  $\dfrac{kq_1 q_2}{r^{3}}$
PE of a point charge
$U = q V$
Dipole moment
$p = q d$
Q1MCQDipole moment
The electric dipole moment is:
- A
  $qd$
- B
  $\dfrac{q}{d}$
- C
  $q+d$
- D
  $qd^{2}$
Torque on a dipole
$τ = p \times E, τ = pE sin θ$
Q1MCQTorque on dipole
The torque on a dipole in a field is:
- A
  $pE\sin\theta$
- B
  $pE\cos\theta$
- C
  $pE$
- D
  $\dfrac{pE}{\sin\theta}$
PE of a dipole
$U = - p \cdot E = - pE cos θ$
Q1MCQPE of dipole
The potential energy of a dipole in a field is:
- A
  $-pE\cos\theta$
- B
  $pE\cos\theta$
- C
  $pE\sin\theta$
- D
  $-pE$
Energy density
$u = \frac{1}{2} ε_{0} E^{2}$
Q1MCQEnergy density
The electrostatic energy density is:
- A
  $\tfrac12\varepsilon_0 E^{2}$
- B
  $\varepsilon_0 E^{2}$
- C
  $\tfrac12\varepsilon_0 E$
- D
  $\dfrac{E^{2}}{2\varepsilon_0}$
Electrostatic pressure
$P = \frac{σ ^{2}}{2 ε _{0}}$
Q1MCQElectrostatic pressure
The pressure on a charged conductor's surface is:
- A
  $\dfrac{\sigma^{2}}{2\varepsilon_0}$
- B
  $\dfrac{\sigma}{2\varepsilon_0}$
- C
  $\dfrac{\sigma^{2}}{\varepsilon_0}$
- D
  $\sigma^{2}\varepsilon_0$
Self energy of a shell
$U = \frac{k Q ^{2}}{2 R}$
Q1MCQSelf energy shell
The self energy of a charged shell is:
- A
  $\dfrac{kQ^{2}}{2R}$
- B
  $\dfrac{3kQ^{2}}{5R}$
- C
  $\dfrac{kQ^{2}}{R}$
- D
  $\dfrac{kQ^{2}}{4R}$
Self energy of a solid sphere
$U = \frac{3 k Q ^{2}}{5 R}$
Q1MCQSelf energy sphere
The self energy of a uniformly charged solid sphere is:
- A
  $\dfrac{3kQ^{2}}{5R}$
- B
  $\dfrac{kQ^{2}}{2R}$
- C
  $\dfrac{kQ^{2}}{R}$
- D
  $\dfrac{2kQ^{2}}{5R}$
Field near a conductor
$E = \frac{σ}{ε _{0}}$
Q1MCQField near conductor
The field just outside a conductor with surface density $\sigma$ is:
- A
  $\dfrac{\sigma}{\varepsilon_0}$
- B
  $\dfrac{\sigma}{2\varepsilon_0}$
- C
  $0$
- D
  $\sigma\varepsilon_0$
Field inside a conductor
$E = 0$
Work in moving a charge
$W = q (V_{B} - V_{A})$
Charge sharing between spheres
$σ_{1} R_{1} = σ_{2} R_{2}$
Q1MCQCharge sharing
When two charged spheres are connected, at equilibrium:
- A
  $\sigma_1 R_1=\sigma_2 R_2$
- B
  $\sigma_1=\sigma_2$
- C
  $Q_1=Q_2$
- D
  $R_1=R_2$
Field of an arc at the centre
$E = \frac{2 k λ}{R} sin (\frac{α}{2})$
Q1MCQArc at centre
The field at the centre of a charged arc (half-angle $\alpha/2$) is:
- A
  $\dfrac{2k\lambda}{R}\sin\!\left(\dfrac{\alpha}{2}\right)$
- B
  $\dfrac{k\lambda}{R}$
- C
  $\dfrac{2k\lambda}{R}$
- D
  $0$

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Elecrostatics formulas

Elecrostatics, every formula

Coulomb's force

Coulomb constant

Electric field

Force on a charge

Field of a line charge

Field of a nonconducting sheet

Field of a conducting sheet

Field on the axis of a ring

Field at the centre of a ring

Field of a shell (outside/inside)

Field inside a solid sphere

Field of a dipole (axial)

Field of a dipole (equatorial)

Field of a dipole (general point)

Electric potential

Potential of a dipole

Potential of a shell

Field from potential

Electric flux

Gauss's law

PE of two charges

PE of a point charge

Dipole moment

Torque on a dipole

PE of a dipole

Energy density

Electrostatic pressure

Self energy of a shell

Self energy of a solid sphere

Field near a conductor

Field inside a conductor

Work in moving a charge

Charge sharing between spheres

Field of an arc at the centre

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