# Problem: What is the magnitude of the electric field at the point(−1.00î −2.00ĵ +4.00k̂ )mif the electric potential in the region is given byV=2.00xyz2, where V is in volts and coordinates x, y, and z are in meters?

###### FREE Expert Solution

In this problem, we have an electric field and electric potential. Thus, we know that that we are dealing with the relationship between the two. The electric field is equal to the derivative of the potential with respect to a given direction.

For a 3D electric field vector:

$\overline{){\mathbf{E}}{\mathbf{=}}{\mathbf{-}}{\mathbf{\nabla }}{\mathbit{V}}}$

Where,

$\overline{){\mathbf{\nabla }}{\mathbf{=}}\frac{\mathbf{\partial }}{\mathbf{\partial }\mathbf{x}}\stackrel{\mathbf{^}}{\mathbf{i}}{\mathbf{+}}\frac{\mathbf{\partial }}{\mathbf{\partial }\mathbf{y}}\stackrel{\mathbf{^}}{\mathbf{j}}{\mathbf{+}}\frac{\mathbf{\partial }}{\mathbf{\partial }\mathbf{z}}\stackrel{\mathbf{^}}{\mathbf{k}}}$

Power rule of derivation:

$\overline{)\frac{\mathbit{d}}{\mathbit{d}\mathbit{t}}\mathbf{\left(}{\mathbit{x}}^{\mathbit{n}}\mathbf{\right)}{\mathbf{=}}{\mathbit{n}}{{\mathbit{x}}}^{\mathbit{n}\mathbf{-}\mathbf{1}}}$

81% (165 ratings) ###### Problem Details

What is the magnitude of the electric field at the point

(−1.00î −2.00ĵ +4.00k̂ )m

if the electric potential in the region is given by

V=2.00xyz2

, where V is in volts and coordinates x, y, and z are in meters?

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Our tutors have indicated that to solve this problem you will need to apply the Electric Field As Derivative of Potential concept. You can view video lessons to learn Electric Field As Derivative of Potential. Or if you need more Electric Field As Derivative of Potential practice, you can also practice Electric Field As Derivative of Potential practice problems.