The discussion revolves around a homework problem related to finding a scalar field H given its gradient in a three-dimensional space. Participants seek resources and clarification on the integration process involved in determining H at a specific point.
Participants do not reach a consensus on the clarity of the question or the approach to solving it, with some expressing confusion and others providing integration steps.
The discussion includes assumptions about the integration process and the nature of the constants involved, which remain unresolved. The exact relationship between the variables and the integration constants is not fully explored.
nimigi said:Hi, its a home work problem, but I am don't loking for an answer, what i need is a resourse to refresh my old mind :)
the question is:
given - H(x1,y1,z1)=H1
gradH=J
J=a*i+b*j+c*k (i roof, j roof, k roof)
find -
H(x2,y2,z2)
thank a lot
cristo said:What's the actual question here? Are you asked to find H such that gradH=J ?
Eighty said:Just integrate. grad H = ai+bj+ck means that dH/dx=a, dH/dy=b, dH/dz=c. Integrating the first gives you H=ax+C(y,z), where C is the constant of integration, which depends on y and z (they are constant with respect to x). Put that into the next equation (dH/dy=b), and continue.