First slide

Electrostatic potential

Question

The electric potential V is given as a function of distance x (metre) by $V = (9 + 10 x - 2 x^{2})$ volt. Then electric field at $x = 1 m$ is

Easy

A

$- 6 \hat{i} \frac{V}{m}$
B

$6 \hat{i} \frac{V}{m}$
C

$4 \hat{i} \frac{V}{m}$
D

$- 4 \hat{i} \frac{V}{m}$

Solution

$V = (9 + 10 x - 2 x^{2}) V$
$∴ \vec{E} = - \frac{d V}{d x} \hat{i} = - (10 - 4 x) \hat{i} = - (10 - 4 \times 1) \hat{i} \frac{V}{m} = - 6 \hat{i} \frac{V}{m}$

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