Electrostatics

You have experienced static electricity -- rubbing a comb through your hair and watching it attract small pieces of paper, or feeling a small shock when touching a metal doorknob in winter. These phenomena are governed by electrostatics, the study of charges at rest.

Electric Charge

There are two types of charge: positive and negative. Like charges repel; unlike charges attract. Charge is quantized: the smallest unit is the charge of an electron, e = 1.6 x 10⁻¹⁹ C.

Charge is conserved: It can be transferred but never created or destroyed.

Coulomb's Law

The force between two point charges is:

F = k q1 q2 / r²

where k = 9 x 10⁹ N m² C⁻² (= 1/4 pi epsilon0), q1 and q2 are charges, and r is the distance between them.

This looks similar to Newton's law of gravitation, but electric force can be both attractive and repulsive.

Electric Field

The electric field at a point is the force experienced by a unit positive charge placed at that point.

E = F/q = kQ/r² (for a point charge Q)

Direction: Away from positive charges, toward negative charges. Unit: N/C or V/m.

Electric Potential

Electric potential at a point is the work done in bringing a unit positive charge from infinity to that point.

V = kQ/r

Unit: Volt (V). Potential difference drives current flow in circuits.

Relation: E = -dV/dr (field is the negative gradient of potential)

Worked Example

Two charges of +2 micro C and -3 micro C are separated by 30 cm. Find the force between them.

Solution:

• q1 = 2 x 10⁻⁶ C, q2 = 3 x 10⁻⁶ C, r = 0.30 m
• F = 9 x 10⁹ x 2 x 10⁻⁶ x 3 x 10⁻⁶ / (0.30)²
• F = 9 x 10⁹ x 6 x 10⁻¹² / 0.09
• F = 54 x 10⁻³ / 0.09 = 0.6 N (attractive, since charges are opposite)

Capacitors (Introduction)

A capacitor stores electric charge and energy. It consists of two conductors separated by an insulator.

Capacitance: C = Q/V (unit: Farad, F)

For a parallel plate capacitor: C = epsilon0 A / d, where A is plate area and d is separation.

Energy stored: U = (1/2) CV²

Key Takeaways

• Coulomb's law: F = kq1q2/r² (similar form to gravitation)
• Electric field E = kQ/r²; Electric potential V = kQ/r
• Field is a vector; potential is a scalar
• Capacitance C = Q/V measures charge storage ability