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Q.

The electric potential in certain region is given as V= $2 x^{2}$ , then the charge density of that region is

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a

$- \frac{4 x}{ε_{_{0}}}$

b

$- \frac{4}{ε_{_{0}}}$

c

$- 2 ε_{_{0}}$

d

$- 4 ε_{_{0}}$

answer is C.

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Detailed Solution

$\vec{E} = - \frac{\partial V}{\partial r} \overset{\land}{i} = 4 x \overset{\land}{i}$

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The electric potential in certain region is given as V= 2x2, then the charge density of that region is