Question: Gradient Field Strength - Magnitude Gradplot


I was wondering someone could help me with something.

Basically I've got a function of f(x,z) that I have plotted which comes from an integration that was taken over a large number of small steps. I have been able to plot this function to determine a Potential Field as a function of x and z. (No Problems so far)

However the next step that I want to be able to do is compute a field form this potential. apologies for my lack of knowing how to input into here as I am fairly new to this. To do this I have:

Field = - Nabla * Potential 

Again no problem, I can plot a gradient field from it which is great using the gradplot command. I beleive this comes as a result of the following:

gradplot = [diff(f,x), diff(f,z)]

HOWEVER I want to be able to plot a Field Strength plot (In essence a Gradient Field Strength) where it takes the magnitude of the vectors at each point. Firstly am I correct in saying that this should be:

Magnitude Field = |F| = sqrt( Fx^2+Fz^2)      where Fx is diff(f,x) and Fz is diff(f,z)


However when I try to compute this, it takes an age to evaluate and doesn't seem to make much progress. I think this may come as a result of computing square roots of large numbers/large decimal places? I was wondering whether there is any command that anyones knows of that would calculate Gradient Field Strength/Magnitude that may solve this issue? Or even who to just compute this Square root?

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