Provide expressions for the electricthe electric potential V(r) at a positionr relativeto a point charge q. Draw a figure showing thecharge and the vector r clearly.positio

Answered: Provide expressions for the electric…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Provide expressions for the electric
the electric potential V(r) at a positionr relative
to a point charge q. Draw a figure showing the
charge and the vector r clearly.
positio

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ELECTRIC FIELD

Let us consider the source point with a charge q at the position A $(x', y', z')$ and the field at point P $(x, y, z)$ .

They are arranged as shown in the figure:

O is the origin.

The position vectors are given as:

$\vec{r}' = x' \hat{x} + y' \hat{y} + z' \hat{z}$

$\vec{r} = x \hat{x} + y \hat{y} + z \hat{z}$

By vector addition we have,

$\vec{r}' + \vec{R} = \vec{r} \Rightarrow \vec{R} = \vec{r} - \vec{r}' = (x - x') \hat{x} + (y - y') \hat{y} + (z - z') \hat{z}$

$|\vec{R}| = \sqrt{{(x - x')}^{2} + {(y - y')}^{2} + {(z - z')}^{2}}$

Thus electric field at P is given by

$\vec{E} (P) = \frac{1}{4 π ε_{0}} \frac{q}{{|\vec{R}|}^{2}}$ $\hat{R}$

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Provide expressions for the electric the electric potential V(r) at a positionr relative to a point charge q. Draw a figure showing the charge and the vector r clearly. positio