Institutt for fysikk, NTNU TFY4155/FY1003: Elektrisitet og magnetisme Spring 2005

Summary, week 2 (January 12)

Quantization of charge [FGT 21.2; YF 21.1; TM 21.1; AF 21.7; LHL 19.1; DJG “Advertisement”]

Electric charge q always appears in integers of the elementary charge e:

q = ne n = 0, ±1, ±2, ...

Matter is made of atoms, consisting of a positively charged nucleus and negatively charged electrons. The nucleus consists of a number of protons and neutrons. A neutral atom with atomic number Z has Z protons in the nucleus and Z electrons around the nucleus. A proton has charge +e, an electron has charge −e, whereas the neutron has zero charge.

Conservation law for charge [FGT 21.2; YF 21.1; TM 21.1; AF 21.8; LHL 19.1; DJG “Advertisement”]

The net charge is always conserved in a closed system.

Coulomb’s law [FGT 21.3; YF 21.3; TM 21.3; AF 21.3; LHL 19.3; DJG 2.1.2]

F = \frac{qq′}{4πε_{0}r^{2}} r̂

= electrostatic force between two point charges q and q′ separated by a distance r. With r̂ directed from q towards q′, F represents the force on q′. The charges q and q′ may be positive or negative. Two positive charges repel each other, two negative charges repel each other, whereas one positive and one negative charge attract each other.

SI unit for electric charge: [FGT 21.3; YF 21.3; TM 21.1; AF 21.4; LHL 19.1; DJG “Advertisement”]

[q] = C (coulomb) The elementary charge: e = 1.6 · 10^{−19} C

The permittivity of vacuum: ε_{0} = 8.85 · 10^{−12} C^{2}/Nm^{2} (1/4πε_{0} ≃ 9 · 10^{9} Nm^{2}/C^{2})

The superposition principle [FGT 21.4; YF 21.3; TM 21.3; AF 21.5; LHL 19.3; DJG 2.1.1]

F_{i} = ∑_{j=1}^{n} F_{ij} = \frac{1}{4πε_{0}} ∑_{j=1}^{n} \frac{q_{j}q_{i}}{r_{ij}^{2}} r̂_{ij}

= electrostatic force on charge q_{i} from charges q_{j} (j = 1, 2, … n) separated by distances r_{ij}.