I want to solve the equation (iv) as a function of E0 as shown in the attached picture. I tried to calculate it using the following code. I am stuck in this problem! please help

Question

Anil Kumar 2018-10-23

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https://ww2.mathworks.cn/matlabcentral/answers/425542-i-want-to-solve-the-equation-iv-as-a-function-of-e0-as-shown-in-the-attached-picture-i-tried-to-c

评论： Torsten 2018-10-23

if true
  % code
end
r=5*10^-9;
V=4/3*pi*r^3;
Nd=10^17;
E0=19;
Ld=18.5*10^-9;
E=E0+1/6*(r/Ld)^2;
Nr=Nd*exp(-(E0+(1/6)*(r/Ld)^2));
eqn=Nd-Nd*exp(-(E0+(1/6)*(r/Ld)^2));
syms E0
eqn=Nd-Nd*exp(-(E0+(1/6)*(r/Ld)^2));
int(eqn,[0,4/3*pi*r^3])

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Torsten 2018-10-23

在 MATLAB Online 中打开

I wonder why your integration is over E0 and not over R:

syms R
eqn = (Nd-Nd*exp(-(E0+(1/6)*(R/Ld)^2)))*4*pi*R^2;
sol = int(eqn,R,0,r)

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Answer 1

madhan ravi 2018-10-23

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在 MATLAB Online 中打开

r=5*10^-9;
V=4/3*pi*r^3;
Nd=10^17;
E0=19;
Ld=18.5*10^-9;
E=E0+1/6*(r/Ld)^2;
Nr=Nd*exp(-(E0+(1/6)*(r/Ld)^2));
eqn=Nd-Nd*exp(-(E0+(1/6)*(r/Ld)^2));
syms E0
eqn=Nd-Nd*exp(-(E0+(1/6)*(r/Ld)^2));
int(eqn,[0,4/3*pi*r^3]) %no errors occurred