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Electric Field Due to Charge Distributions - Approach

The potential...

Question

The potential of the electric field produced at a point $(x, y, z)$ is given at $V = x^{2} + 4 x + 5$ where $x, y, z$ are in meters and $V$ is in volts. What is the intensity of the electric field at $(2, 1, 0)$ ?

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Solution

$V = x^{2} + 4 x + 5$
$V = \int E \cdot d r$
$∴ E = \frac{d}{d r} (V)$
$\Rightarrow E = 2 x + 4$
$\Rightarrow E = (2 \times 2 + 4)$
$\Rightarrow E = 8$ $N / C$
Electric Field at $(2, 1, 0)$

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