RF and Microwave Engineering: Fundamentals of Wireless Communications

2.1 Electric and Magnetic Fields

In this section we introduce mathematical formulas and physical relations for the static case in order to get a visual understanding of electric and magnetic field quantities.

2.1.1 Electrostatic Fields

2.1.1.1 Field Strength and Voltage

Historically it has been known for a long time that electric charges are the origin of electrical phenomena. Charges produce forces upon each other. We distinguish between positive and negative charges. Charges of opposite signs attract each other whereas charges of same sign push each other away. The absolute value of the Coulomb force F_C between two point charges¹ Q₁ and Q₂, separated by a distance r, is given by

2.1

where ε₀ = 8.854 · 10⁻¹² As/(Vm) is the permittivity of free space.

The direction of the Coulomb force is defined by a straight line through both charges (see Figure 2.1a and 2.1b). In the case of three or more charges we can add up the vectors of the forces by the principle of superposition (vector sum in Figure 2.1c).

Figure 2.1 Coulomb forces between (a) two positive charges, (b) two charges of opposite polarity and (c) three charges of equal polarity.

Charges exist in discrete values (integer values of elementary charge e = 1.602 · 10⁻¹⁹ C). However, in practical (macroscopic) engineering configurations ...