Example Electric Field of a Circular Disk of Charge Find the electric field at point P with Cartesian coordinates (0, 0, h) due to a circular disk of radius a and uniform charge Also, evaluate E density ps residing in the x-y plane due to an infinite sheet of charge density ps by letting a → 00. Solution: Building on the expression obtained in Example for the on-axis electric field due to a circular ring of charge. we can determine the field due to the circular disk by treating the disk as a set of concentric rings. A ring of radius r and width dr has an area ds = 2πr dr and contains charge dq=ps ds = 2лpr dr. Upon using this expression in Eq. and also replacing b with r, we obtain the following expression for the field due to the ring: h dE=2 Απερ (γ2 + 11213/2 (2лpr dr). Example cont. The total field at P is obtained by integrating the expression over the limits r = 0 tora: E=2 Psh 280 r dr (2+2)3/2 Ps h = ±2 260 a²+h2. E=1 E P=(0, 0, h) h dq=2xpr dr a Circular disk of charge with surface charge density ps. The electric field at P= (0, 0. h) points along the z-direction (Example 4-5). E P=(0, 0, h) Cont. with the plus sign for h > 0 (P above the disk) and the minus sign when h<0 (P below the disk). For an infinite sheet of charge with a = 0, E=+ Ps 260 (infinite sheet of charge). We note that for an infinite sheet of charge E is the same at all points above the x-y plane, and a similar statement applies for minte below the x-y plane. dy=2xpr dr 21 Circular disk of charge with surface charge