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The electric potential in the region of space is given by: $V (x) = A + B x + C x^{2}$ , where v is volts, x is in meters and A,B,C are constants. Then,

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$\vec{E}$ varies linearly with x

The unit of $\vec{E}$ is N/C.

The electric field $\vec{E}$ in this region is constant.

$\vec{E}$ is in the negative x-direction.

answer is A.

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Detailed Solution

$E = - (d V / d x) = - B - 2 C x$

i.e., E varies linearly with x and is along negative x-direction. It is also clear that B has dimensions or units of E, i.e., $N C^{- 1}$

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