Relationships Between Force, Field, Energy, Potential Video Lessons

Concept

Problem: Suppose you have a uniform Electric field with magnitude of 5 V/m in the +x direction. (a) What can you say about potential difference between two points separated by a distance of 2 m along the x-axis? (b) What can you say about potential difference between two points separated by a distance of 3 m along the y-axis?

FREE Expert Solution

Electric field:

$\overline{)\stackrel{\mathbf{⇀}}{{\mathbf{E}}_{\mathbf{x}}}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{\partial }\mathbf{V}}{\mathbf{\partial }\mathbf{x}}}$

(a)

Potential difference, ΔV:

$\begin{array}{rcl}\mathbf{|}\mathbf{∆}\mathbf{V}\mathbf{|}& \mathbf{=}& \mathbf{|}\mathbf{-}\mathbf{\int }\stackrel{\mathbf{⇀}}{{\mathbf{E}}_{\mathbf{x}}}\mathbf{·}\stackrel{\mathbf{⇀}}{{\mathbf{d}}_{\mathbf{x}}}\mathbf{|}\mathbf{=}\mathbf{|}\mathbf{-}\mathbf{E}\mathbf{×}\mathbf{d}\mathbf{|}\\ & \mathbf{=}& \mathbf{|}\mathbf{-}\mathbf{5}\mathbf{×}\mathbf{2}\mathbf{|}\end{array}$

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Problem Details

Suppose you have a uniform Electric field with magnitude of 5 V/m in the +x direction. (a) What can you say about potential difference between two points separated by a distance of 2 m along the x-axis? (b) What can you say about potential difference between two points separated by a distance of 3 m along the y-axis?