Simple Nature - Light and Matter

know that there is a delay in time before a change in the configuration of mass and charge inone corner of the universe will make itself felt as a change in the forces experienced far away.We imagine the outward spread of such a change as a ripple in an invisible universe-filling fieldof force.As an alternative to our earlier energy-based definition, we can define the gravitational fieldat a given point as the force per unit mass exerted on objects inserted at that point, and likewisethe electric field is defined as the force per unit charge. These fields are vectors, and the fieldsgenerated by multiple sources add according to the rules of vector addition.The relationship between the electric field and the voltage is∂V∂x = −E x∂V∂y = −E y∂V∂z = −E z ,which can be notated more compactly as a gradient,E = −∇V .Fields of force contain energy, and the density of energy is proportional to the square of themagnitude of the field,dU g = − 18πG g2 dvdU e = 18πk E2 dvdU m ∝ B 2 dvThe equation for the energy stored in the magnetic field is given explicitly in the next chapter;for now, we only need the fact that it behaves in the same general way as the first two equations:the energy density is proportional to the square of the field. In the case of static electric fields,we can calculate potential energy either using the previous definition in terms of mechanicalwork or by calculating the energy stored in the fields. If the fields are not static, the old methodgives incorrect results and the new one must be used.andCapacitance, C, and inductance, L, are defined asU C = 12C q2U L = L 2 I2 ,measured in units of farads and henries, respectively. The voltage across a capacitor or inductoris given byV C = q C958 Chapter Appendix 6: Summary