T1 Figure 3.3: Demonstration of path independence of the electric field line integral Of course, the large-scale form(3.29 )also implies the path-independence of work in the electrostatic field. Indeed, we may pass an arbitrary closed contour r through Pr and P2 and then split it into two pieces TI and T2 as shown in Figure 3.3. Since EdI=-Q/EdI+0/EdI=0. 1-r2 we hav eE.dI=-Q/E We sometimes refer to p(r) as the absolute electrostatic potential. Choosing a suitable reference point Po at location ro and writing the potential difference as V21=[(r2)-Φ(ro)-[Φ(ri)-中(ro)] we can justify calling p(r) the absolute potential referred to Po. Note that Po might describe a locus of points, rather than a single point, since many points can be at the same value of E found from( 3.30), for simplicity we often choose ro such that (ro)=0. potential. Although we can choose any reference point without changing the result Several properties of the electrostatic potential make lectric fields. We know that, at equilibrium, the electrostatic field within a conducting body must vanish. By(3. 30) the potential at all points within the body must therefore have the same constant value. It follows that the surface of a conductor is an equipotential surface: a surface for which p(r) is constant As an infinite reservoir of charge that can be tapped through a filamentary conductor the entity we call"ground"must also be an equipotential object. If we connect a con- ductor to ground, we have seen that charge may flow freely onto the conductor. Since no work is expended, "grounding a conductor obviously places the conductor at the same absolute potential as ground. For this reason, ground is often assigned the role as the potential reference with an absolute potential of zero volts. Later we shall see that for sources of finite extent ground must be located at infinit ②2001 by CRC Press LLCFigure 3.3: Demonstration of path independence of the electric field line integral. Of course, the large-scale form (3.29)also implies the path-independence of work in the electrostatic field. Indeed, we may pass an arbitrary closed contour  through P1 and P2 and then split it into two pieces 1 and 2 as shown in Figure 3.3. Since −Q 1−2 E · dl = −Q 1 E · dl + Q 2 E · dl = 0, we have −Q 1 E · dl = −Q 2 E · dl as desired. We sometimes refer to (r) as the absolute electrostatic potential. Choosing a suitable reference point P0 at location r0 and writing the potential difference as V21 = [(r2) − (r0)] − [(r1) − (r0)], we can justify calling (r) the absolute potential referred to P0. Note that P0 might describe a locus of points, rather than a single point, since many points can be at the same potential. Although we can choose any reference point without changing the resulting value of E found from (3.30), for simplicity we often choose r0 such that (r0) = 0. Several properties of the electrostatic potential make it convenient for describing static electric fields. We know that, at equilibrium, the electrostatic field within a conducting body must vanish. By (3.30)the potential at all points within the body must therefore have the same constant value. It follows that the surface of a conductor is an equipotential surface: a surface for which (r) is constant. As an infinite reservoir of charge that can be tapped through a filamentary conductor, the entity we call “ground” must also be an equipotential object. If we connect a con￾ductor to ground, we have seen that charge may flow freely onto the conductor. Since no work is expended, “grounding” a conductor obviously places the conductor at the same absolute potential as ground. For this reason, ground is often assigned the role as the potential reference with an absolute potential of zero volts. Later we shall see that for sources of finite extent ground must be located at infinity.