Electric field:

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

**(a)**

Potential difference, ΔV:

$\begin{array}{rcl}\mathbf{|}\mathbf{\u2206}\mathbf{V}\mathbf{|}& \mathbf{=}& \mathbf{|}\mathbf{-}\mathbf{\int}\stackrel{\mathbf{\rightharpoonup}}{{\mathbf{E}}_{\mathbf{x}}}\mathbf{\xb7}\stackrel{\mathbf{\rightharpoonup}}{{\mathbf{d}}_{\mathbf{x}}}\mathbf{|}\mathbf{=}\mathbf{|}\mathbf{-}\mathbf{E}\mathbf{\times}\mathbf{d}\mathbf{|}\\ & \mathbf{=}& \mathbf{|}\mathbf{-}\mathbf{5}\mathbf{\times}\mathbf{2}\mathbf{|}\end{array}$

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?

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