2.1 Basic Physics Review
This section reviews the concepts of electric charge and electric potential (also known as voltage). Electric charge is a measure of quantity of electricity and can have positive or negative values. Recall that matter is made up of atoms which, in turn, are made of negatively charged electrons, positively charged protons, and neutrally charged neutrons. Recall from your physics class that electrical charges exert forces on each other analogous to the way masses attract each other and give us gravity. More than one engineering student has reported that mass and gravity are more familiar and less abstract concepts than charge and electric potential. This may be pervasive: we may not understand relativistic effects and curvature in the space-time continuum, but all engineering students are comfortable applying Newton’s law of gravitation to compute the attractive force between two masses in the Universe. Many engineers use these concepts to analyze material strain and build bridges and skyscrapers. Even though light (electromagnetic energy) is visible all around us, electromagnetics just seems to be harder to digest. So we start this discussion with mass and gravity and then move to the analogous context, where the formulas are nearly the same, and we examine charge and electric potential. Simple expressions for gravitational attraction as well as gravitational and electric potential are given below as a way to help illustrate concepts. We are not interested in computing these quantities in any detail in this course, however.
Gravitational attraction. Recall that objects having mass exert attractive forces on one-another via the uniform law of gravitational attraction. Assume we have a small “test mass”, , separated from another small mass, by distance . As illustrated in Fig. 2.1, mass exerts an attractive force on mass given by
(1)
in units of Newtons (N) where the gravitational constant . (Likewise, mass exerts an attractive force on mass . However, let us concern ourselves only with the force on our test mass, .)
If we let , the mass of the Earth, and we let , the radius of the Earth, and we insert these values into equation (1) then we have
(2)
which is the familiar equation for the attractive force due to gravity, where . This is depicted in Fig. 2.1 and is really an approximation, valid for objects close to the Earth’s surface. In this figure, the Earth’s surface is shown as being flat rather than spherical; this is due to the fact that the Earth’s radius is so large that any sketch of its surface up close appears flat.
Gravitational potential energy. Now consider test mass, , at two different heights above the surface of the Earth, and as shown. At these two heights, the mass has potential energy
(3)
in joules (J) and
(4)
as illustrated in Fig. 2.2
The work needed to lift the mass from height hA to height hB is
(5)
Thus represents the amount of energy that would need to be transferred into the mass at height in order