Electric Fields with Calculus Video Lessons

Concept

# Problem: The electric potential along the x-axis is V=100e-2x mV, where x is in meters.Part AWhat is Ex at x=1.0m?Express your answer as an integer and include the appropriate units.Part BWhat is Ex at x=2.4m?Express your answer to two significant figures and include the appropriate units.

###### FREE Expert Solution

Electric field E:

$\overline{){\mathbf{E}}{\mathbf{=}}{\mathbf{-}}\frac{\mathbf{d}\mathbf{V}}{\mathbf{d}\mathbf{x}}}$

Substituting:

$\begin{array}{rcl}\mathbf{E}\mathbf{\left(}\mathbf{x}\mathbf{\right)}& \mathbf{=}& {\mathbf{-}}{\mathbf{100}}\frac{\mathbf{d}\mathbf{\left(}{\mathbf{e}}^{\mathbf{-}\mathbf{2}\mathbf{x}}\mathbf{mV}\mathbf{\right)}}{\mathbf{dx}}\\ & \mathbf{=}& \mathbf{200}{\mathbf{e}}^{\mathbf{-}\mathbf{2}\mathbf{x}}\end{array}\phantom{\rule{0ex}{0ex}}$

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###### Problem Details

The electric potential along the x-axis is V=100e-2x mV, where x is in meters.

Part A

What is Ex at x=1.0m?