Question

Problem 8: Solve problem 21 on page 317 of Gilat's book 1. Program a function that calculates the integrand. 2. Use the MATLAB quad function in order to calculate the integral numerically. 21. The electric field E due to a charged circular disk at a point at a distance z along the axis of the disk is given by where σ is the charge density, , is the permittivity constant, e.-8.85 x 10-12 CON m2) and R is the radius of the disk. Determine the electric field at a point located 5 cm from a disk with a radius of 6 cm, charged with σ-300 μC/m2.

Answer 1

ANSWER
clear all;

close all;

% Given Electric Field E

ilon IRぱ+ r2)-22r dr 96%E= 4 * eps

%%%%%%%%%%%%%%%%%%%%%%% Given values %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

row = 300*10^(-6) % C/m

row = 3.0000e-04

z = 0.05 %m

z = 0.0500

epsilon = 8.85*10^(-12)

epsilon = 8.8500e-12

R = 0.06

R = 0.0600

%%%%%%%%%%%%%%%%%%%%% E = K * Q %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%% K = (2*row*z/4*epsilon)%%%%%%%%%%%%%%%%%%%%%%%%

K = (2*row*z)/(4*epsilon)

K = 8.4746e+05

%%%%%%%%%%%%%%%%%%% Q &&&&&&&&&&&&&&&&&

F = @(r) r.*(z.^2+r.^2).^(-3/2)

F = function_handle with value:

@(r)r.*(z.^2+r.^2).^(-3/2)

Q = quad(F,0,R)

Q = 7.1963

%%%%%%%%%%%%%%%%%%% E = K*Q %%%%%%%%%%%%%%%%%%%%%%%

E = K*Q

E = 6.0986e+06 = 6.0986 x 10^6 Volt/meter

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