Class 12 Physics Electric Field and Charge Class Formula Sheet

• Net charge when there is a gain or loss of n electrons: $Q=ne$
• Net charge passing through a circuit in time t sec: $Q=\mathrm{it}$
• Net charge in a system of n individual charges: $Q=q_1+q_2+q_3+\dots +q_n$

• Coulomb Force between two charges separated by distance (r): $F=\frac{1}{4\pi \epsilon ₀}\frac{q_1{q}_2}{r^2}$
• Vector Form of Coulomb's Law: $F=\frac{1}{4\pi \epsilon ₀}\frac{q_1{q}_2}{r^3}\stackrel{\to }{r}$
• Net force for a system of multiple charges: $${\mathbf{F}}_1={\mathbf{F}}_{12}+{\mathbf{F}}_{13}+\dots +{\mathbf{F}}_{1n}=\frac{1}{4\pi {\epsilon }_0}[\frac{q_1{q}_2}{r_{12}^2}{\stackrel{}{\mathbf{r}}}_{12}+\frac{q_1{q}_3}{r_{13}^2}{\stackrel{}{\mathbf{r}}}_{13}+\dots +\frac{q_1{q}_n}{r_{1n}^2}{\stackrel{}{\mathbf{r}}}_{1n}]$$

• Electric field due to a point charge, which exerts an electrostatic force (F) on a test charge (q_o) $E=\frac{F}{q_0}$
• Electric field due to a point charge (q) at a distance (r): $E=\frac{1}{4\pi \epsilon ₀}\frac{q}{r^2}$
• Electric field due to a ring of charge of radius (R) and total charge (Q) at a distance x from the centre on the axial line.

$$E=\frac{1}{4\pi {\epsilon }_0}\frac{Qx}{{(R^2+x^2)}^{3/2}}$$

• Line charge density: $\lambda =\frac{Q}{L}$
• Surface charge density: $\sigma =\frac{Q}{A}$
• Volume charge density: $\rho =\frac{Q}{V}$

$\Phi =E\cdot A=\mathrm{EA}cos\theta$

$\Phi =\frac{q}{\epsilon }$

• Electric field due to an infinite line charge: ( λ is linear charge density)

  $E=\frac{\lambda }{2\pi \epsilon ₀r}$

  Electric field Intensity due to an infinite plane sheet of charge: ( σ is surface charge density)

  $E=\frac{\sigma }{2\epsilon ₀}$

  Electric field Intensity due to a uniformly charged conducting sphere

  • Outside: $E=\frac{1}{4\pi \epsilon ₀}\frac{Q}{r^2}$
  • On Surface: $E=\frac{1}{4\pi \epsilon ₀}\frac{Q}{R^2}$
  • Inside $E=0$

  Electric Field due to a non-conducting charged sphere

  • Outside of the sphere: $E=\frac{1}{4\pi \epsilon ₀}\frac{Q}{r^2}$
  • On the surface: $E=\frac{1}{4\pi \epsilon ₀}\frac{Q}{R^2}$
  • Inside the sphere: $E=\frac{1}{4\pi \epsilon 0_{}}\frac{Qr}{R^3}$

Dipole moment: $p=q\times d$

Electric Field Due to Electric Dipole

• On Axial Line: $E=\frac{1}{4\pi \epsilon ₀}\frac{2p}{r^3}$
• On the Equatorial Line: $E=\frac{1}{4\pi \epsilon ₀}\frac{p}{r^3}$

Torque due to an electric dipole when placed in an electric field of intensity (E):

$\tau =pEsin\theta$

Potential Energy due to an electric dipole: (Negative of work done by dipole in electric field E)

$U=-pEcos\theta$