Electrostatics

Electric Charge

• Charge of an Electron: \(-e\), where \(e\) is the elementary charge

Coulomb's Law

• Force between two point charges: \(F = k\frac{q_1q_2}{r^2}\), where \(k\) is the Boltzmann's Constant

Electric Field

• Vector field surrounding an electric charge that exerts force on other charges
• Electric field strength \(E = \frac{F}{q} = k \frac{Qq}{r^2} \cdot{1}{q} = k \frac{Q}{r^2}\)
• \(F\) and \(E\) experienced by \(q\) in electric field due to \(Q\)
• SI unit of \(E\): \(\mathrm{NC^{-1}}\)

Electric Potential

• Work done moving a unit positive charge from a reference point to a specific point: \(V = \frac{W}{q}\)
• Typical reference point: Earth or a point at infinity 
• Work done moving \(q\) across \(\triangle V\) is \(W = q \triangle V\)
• Electric potential due to a charge \(Q\) at distance \(r\) from the charge is \(V = \frac{1}{4 \pi \epsilon_{0}} \cdot \frac{Q}{r}\)
• Electrical potential energy of a charge \(q\) at a point with potential \(V\) is \(U = q V\)
• Electric field \(E\) between two parallel plates with distance \(d\) apart and with potential difference \(V\) is uniform: \(E = \frac{V}{d}\)