Electric field from potential and coordinate

AI Thread Summary
To find the electric field from the given potential function V(x,y,z) = 3x^2 + 2y + 5, the gradient must be calculated using E = -∇V. The x-component of the electric field is derived as -6x, and the full electric field can be determined by taking the partial derivatives of V with respect to x, y, and z. The initial attempt at solving the problem incorrectly calculated the electric field as 32 N/C. Understanding the gradient and its relation to electric potential is crucial for solving such problems.
axgalloway
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Homework Statement



I am given V(x,y,z) = 3x^2 + 2y + 5 and I am given s = (5,3,1), so what is the electric field?

Homework Equations


V= Es


The Attempt at a Solution


I really have no idea. What I tried:

Derivative of V(x,y,z) = 6x+2
so E = 32 N/C?

Really I just don't understand the math necessary. How is it done?
 
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What you really need to do is take the gradient of the potential function:

E = - \nabla V

You'll find the components of the electric field by taking the partial derivative with respect to each variable. Thus the x-component of the field will be -6x.

See: http://hyperphysics.phy-astr.gsu.edu/Hbase/gradi.html"
 
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