edge effects,and the non-uniform fields near the edge are called the fringing fields.In Figure 5.2.1 the field lines are drawn by taking into consideration edge effects.However, in what follows,we shall ignore such effects and assume an idealized situation,where field lines between the plates are straight lines. In the limit where the plates are infinitely large,the system has planar symmetry and we can calculate the electric field everywhere using Gauss's law given in Eq.(4.2.5): ∯EdA=9 80 By choosing a Gaussian "pillbox"with cap area 4'to enclose the charge on the positive plate(see Figure 5.2.2),the electric field in the region between the plates is EA'-4-A E=o (5.2.1) 6080 Eo The same result has also been obtained in Section 4.8.1 using superposition principle. Gaussian surface +0 A Path of intergration Figure 5.2.2 Gaussian surface for calculating the electric field between the plates. The potential difference between the plates is AV=V.-V.=-f.E.ds=-Ed (5.2.2) where we have taken the path of integration to be a straight line from the positive plate to the negative plate following the field lines(Figure 5.2.2).Since the electric field lines are always directed from higher potential to lower potential,V<V..However,in computing the capacitance C,the relevant quantity is the magnitude of the potential difference: |△V=Ed (5.2.3) and its sign is immaterial.From the definition of capacitance,we have 4edge effects, and the non-uniform fields near the edge are called the fringing fields. In Figure 5.2.1 the field lines are drawn by taking into consideration edge effects. However, in what follows, we shall ignore such effects and assume an idealized situation, where field lines between the plates are straight lines. In the limit where the plates are infinitely large, the system has planar symmetry and we can calculate the electric field everywhere using Gauss’s law given in Eq. (4.2.5): enc S 0 q d ε ⋅ = ∫∫ E A JG JG w By choosing a Gaussian “pillbox” with cap area A′ to enclose the charge on the positive plate (see Figure 5.2.2), the electric field in the region between the plates is enc 0 0 q A' EA' E 0 σ σ ε ε ε = = ⇒ = (5.2.1) The same result has also been obtained in Section 4.8.1 using superposition principle. Figure 5.2.2 Gaussian surface for calculating the electric field between the plates. The potential difference between the plates is V V V d Ed − − + + ∆ = − = − ⋅ = − ∫ E s G G (5.2.2) where we have taken the path of integration to be a straight line from the positive plate to the negative plate following the field lines (Figure 5.2.2). Since the electric field lines are always directed from higher potential to lower potential, V− < V+ . However, in computing the capacitance C, the relevant quantity is the magnitude of the potential difference: | V∆ | E = d (5.2.3) and its sign is immaterial. From the definition of capacitance, we have 4