- #1
CraigH
- 222
- 1
Homework Statement
a)Calculate the total charge a square capacitor plate would have with width x, height y, thickness z, and charge density f(x,y,z) = 1+x+y
b)Calculate the total charge a sphere would have with radius r, and charge density f(x,y,z)=x+y+z
Use the triple integration seen in gauss' theorem and show all working.
Homework Equations
[itex]Q= \int\int\int\rho .dv[/itex]
[itex]\rho = Charge Density[/itex]
[itex]v=Volume[/itex]
The Attempt at a Solution
a)
[itex]\int\int\int f(x,y,z) .dv[/itex]
[itex]\int\int\int f(x,y,z) .dx.dy.dz[/itex]
[itex]\int\int\int 1+x+y .dx.dy.dz[/itex]
[itex]\int\int x + x^2 + yx .dy.dz[/itex]
[itex]\int xy + (x^2)y + x(y^2) .dz[/itex]
[itex]Charge = xyz +(x^2)yz + x(y^2)z[/itex]
//I think this one is correct?
b)
[itex]\int\int\int x+y+z .dx.dy.dz[/itex]
//I get stuck here with this one because it is a sphere and not just a simple shape
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