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Standard XII

Physics

Dimensional Analysis

The potential...

Question

The potential in electric field varies as $V = - 2 a y^{2} - c y$ with respect to y-coordinate (where a and c are constant). The volume charge density p(y) in space will be

2 a ϵ_{0}

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4 a ϵ_{0}

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a ϵ_{0}

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3 a ϵ_{0}

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Solution

The correct option is B $4 a ϵ_{0}$
$V = - 2 a y^{2} - c y$
The volume charge density
$\frac{d v}{d y} = 4 a y$
$= 4 a ϵ_{0}$ (where $y = ϵ_{0}$ )

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Similar questions

Q. In a certain region of space, the electric potential is

V (x, y, z) = A x y - B x^{2}

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A, B a n d C

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Q. In a certain region of space, the electric potential is

V (x, y, z) = A x y - B x^{2}

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The electric potential inside a charged sphere varies with the distance 'r' from its centre as V = a - br $^{3}$ , where 'a' and 'b' are positive constant. Then select the correct statement(s) from the following.

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Q. The electric potential varies in space according to the relation

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The potential in electric field varies as V=−2ay2−cy with respect to y-coordinate (where a and c are constant). The volume charge density p(y) in space will be

The correct option is B 4aϵ0V=−2ay2−cyThe volume charge density dvdy=4ay =4aϵ0 (where y=ϵ0)

The potential in electric field varies as $V = - 2 a y^{2} - c y$ with respect to y-coordinate (where a and c are constant). The volume charge density p(y) in space will be

The correct option is B $4 a ϵ_{0}$
$V = - 2 a y^{2} - c y$
The volume charge density
$\frac{d v}{d y} = 4 a y$
$= 4 a ϵ_{0}$ (where $y = ϵ_{0}$ )