Electric Field As Derivative of Potential Video Lessons

Concept

# Problem: In a certain region of space, the electric potential is V(x,y,z) = Axy - Bx^2 + Cy , where A, B, and C are positive constants.a) Calculate the x-component of the electric field.Express your answer in terms of the given quantities.b) Calculate the y-component of the electric field.Express your answer in terms of the given quantities.c) Calculate the z-component of the electric field.Express your answer in terms of the given quantities.d) At which point is the electric field equal to zero?

###### FREE Expert Solution

The different components of the electric field:

$\overline{)\begin{array}{rcl}{\mathbf{E}}_{\mathbf{x}}& {\mathbf{=}}& \mathbf{-}\frac{\mathbf{\partial }\mathbf{V}}{\mathbf{\partial }\mathbf{x}}\\ {\mathbf{E}}_{\mathbf{y}}& {\mathbf{=}}& \mathbf{-}\frac{\mathbf{\partial }\mathbf{V}}{\mathbf{\partial }\mathbf{y}}\\ {\mathbf{E}}_{\mathbf{z}}& {\mathbf{=}}& \mathbf{-}\frac{\mathbf{\partial }\mathbf{V}}{\mathbf{\partial }\mathbf{z}}\end{array}}$

a)

Let's use the first equation from the list above.

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###### Problem Details

In a certain region of space, the electric potential is V(x,y,z) = Axy - Bx^2 + Cy , where A, B, and C are positive constants.

a) Calculate the x-component of the electric field.

b) Calculate the y-component of the electric field.