Project 5.3 A positive surface charge density of magnitude = 4x10-12 coul/m2 extends infi- nitely in the x-y plane as shown in Figure P5.3a. Using a method similar to what was described in Section 5.4 (show your work), define a differential charge element d(2-0 dyax and then find the resulting electric field by integrating over the sheet of charge for X, = [- ,00] , y,- ,, and z, 4 (P5.3a) 4 Z- z 4 (P5.30 Measurement point dE Sheet charge with surface charge density coul/m 2 Differential charge element dxdy Sheet charge with surface charge density coul/m2 located at zp 1 mm Sheet charge with surface charge density- coul/m 2 located at zp1 mm (lb) Figure P5.3 (a) The differential electric field dE at observation point T due to a differential sheet charge element ddy located on the x-y plane. (b) Two parallel and oppositely charged sheet charges located on the planes z = +1mm and z =-1 mm. 1. Write a MATLAB program using the d blquad function to calculate , Ey, and E, at the following points: 2[0, 0, 2 x 10-3] (above the plate) x, , y,, z.-[ 30x10-3,-5x 10-3, 1 2x 10-3 ] (below the plate) Assume that 10 is a good enough approximation for infinity. Note that by symmetry, the x and y components of the field should integrate to zero (or close to it). Confirm this result. 2. Now, assume that there are two sheet charges in the planes parallel to the x-y plane: the first sheet located at z, -+1 mm with surface charge density -4x 10-12 coul/m 2 and the second sheet located at z,--1 mm and oppo- sitely charged with surface charge density -4 x 10-12 coul/m2 (see Figure P5.3b). Find the electric field via superposition by calculating the electric field 150 Numerical and Analytical Methods with MATLAB separately for each sheet and then adding them together. Find E E, and E, for the these three points: [0, 0, 2 x 10 3] x, y, z-[10x 10-3, 0,-0.5x 10-3] x,,y,,z, _ [ 30 x 10-3 , _ 5x 10-3, 12 x 10-3 ] above the plates) (between the plates) (below the plates) x, y,' z, Print out the results. Do these results make sense? Project 5.3 A positive surface charge density of magnitude = 4x10-12 coul/m2 extends infi- nitely in the x-y plane as shown in Figure P5.3a. Using a method similar to what was described in Section 5.4 (show your work), define a differential charge element d(2-0 dyax and then find the resulting electric field by integrating over the sheet of charge for X, = [- ,00] , y,- ,, and z, 4 (P5.3a) 4 Z- z 4 (P5.30 Measurement point dE Sheet charge with surface charge density coul/m 2 Differential charge element dxdy Sheet charge with surface charge density coul/m2 located at zp 1 mm Sheet charge with surface charge density- coul/m 2 located at zp1 mm (lb) Figure P5.3 (a) The differential electric field dE at observation point T due to a differential sheet charge element ddy located on the x-y plane. (b) Two parallel and oppositely charged sheet charges located on the planes z = +1mm and z =-1 mm. 1. Write a MATLAB program using the d blquad function to calculate , Ey, and E, at the following points: 2[0, 0, 2 x 10-3] (above the plate) x, , y,, z.-[ 30x10-3,-5x 10-3, 1 2x 10-3 ] (below the plate) Assume that 10 is a good enough approximation for infinity. Note that by symmetry, the x and y components of the field should integrate to zero (or close to it). Confirm this result. 2. Now, assume that there are two sheet charges in the planes parallel to the x-y plane: the first sheet located at z, -+1 mm with surface charge density -4x 10-12 coul/m 2 and the second sheet located at z,--1 mm and oppo- sitely charged with surface charge density -4 x 10-12 coul/m2 (see Figure P5.3b). Find the electric field via superposition by calculating the electric field 150 Numerical and Analytical Methods with MATLAB separately for each sheet and then adding them together. Find E E, and E, for the these three points: [0, 0, 2 x 10 3] x, y, z-[10x 10-3, 0,-0.5x 10-3] x,,y,,z, _ [ 30 x 10-3 , _ 5x 10-3, 12 x 10-3 ] above the plates) (between the plates) (below the plates) x, y,' z, Print out the results. Do these results make sense
