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eminem14
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Homework Statement
A volume charge density of ρv=1/r^2 μC/m^3 exists in the region bounded by 1.0m<r<1.5m. Find the potential difference between point A(3.0,4.0,12.0) and point B(2.0,2.0,2.0)
Homework Equations
dQ=(ρv)dv dV=[dQ/(4∏ε0]*norm(R) where R is position vector of a point charge relative to observation point A or B.
dv=r^2 *sinθ*dr*dθ*d∅
x=rsinθ*cos∅ ; y=r*sinθ*sin∅ ; z=r*cosθ (transformations of coordiantes from spherical to cartesian
Ar= Ax*sinθ*cos∅ + Ay*sinθ*sin∅ + Az*cosθ (obtaining radial component(Ar) from cartesian components Ax,Ay and Az)
The Attempt at a Solution
I attempted to first find the voltage at A and B and subtract them from each other by doing the following:
1. Finding dQ=[1/(r^2)]*r^2 *sinθ*dr*dθ*d∅=sinθ*dr*dθ*d∅
2. Therefore, dV=sinθ*dr*dθ*d∅*norm(R)
3. Rx= r*sinθ*cos∅ -3 Ry=r*sinθ*sin∅ -4 Rz=r*cosθ -12 (trasformation of spherical components to cartesian coordinates minus the coordinates of A.
Problem:
I am finding difficulty in getting the norm of R because I can't obtain the unit vector of R which means I can't evaluate the integral to find V. I assumed that the voltage would only have a radial component given the method used in the MATLAB solution I have(not sure though and don't know why). Also given the subtractions shown in point 3, i couldn't integrate because the terms under the root for the magnitude of R can't be simplified.
Please help and thank u in advance
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