(D) The relationship between electric field $E$ and potential $V$ is given by $E = -\frac{dV}{dx}$.Given the potential function $V = 8x^2 + 2$.Differe

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(D) The relationship between electric field $E$ and potential $V$ is given by $E = -\frac{dV}{dx}$.Given the potential function $V = 8x^2 + 2$.Differentiating with respect to $x$,we get $\frac{dV}{dx} = \frac{d}{dx}(8x^2 + 2) = 16x$.Thus,the electric field $E_x = -16x$.At the point $(-4, 0)$,the $x$-coordinate is $x = -4$.Substituting this value into the expression for $E_x$,we get $E_x = -16(-4) = 64 \, V/m$.The magnitude of the electric field is $|E_x| = 64 \, V/m$.

Class 12 Physics Electric Potential and Capacitance Relation between Electric Field and Potential and Potential Gradient

Easy

In a certain region of space,the variation of potential with distance from the origin as we move along the $x$-axis is given by $V = 8x^2 + 2$,where $x$ is the $x$-coordinate of a point in space. The magnitude of the electric field at a point $(-4, 0)$ is .......... $V/m$.

A
$16$
B
$32$
C
$48$
D
$64$

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Class 12

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Chapter

Electric Potential and Capacitance

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Relation between Electric Field and Potential and Potential Gradient

Two large plane parallel conducting plates are kept $10 \ cm$ apart as shown in the figure. The potential difference between them is $V$. The potential difference between the points $A$ and $B$ (shown in the figure) is

MediumJEE MAIN 2025

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The diagram below shows electric field lines in a region of space. Which of the following diagrams best shows the variation with distance $d$ of the potential $V$ along the line $XY$ as we move from $X$ to $Y$?

Medium

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Let $V$ and $E$ be the potential and electric field intensity at a point,respectively. Then:

Easy

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If the electric potential is given by $V = (5x^2 + 10x - 9) \ V$,what is the electric field at $x = 1 \ m$ in $V/m$?

Medium

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$A$ uniform electric field having a magnitude $E_0$ and direction along the positive $X$-axis exists. If the potential $V$ is zero at $x = 0$,then its value at $x = +x$ will be:

Easy

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In a certain region of space,the variation of potential with distance from the origin as we move along the $x$-axis is given by $V = 8x^2 + 2$,where $x$ is the $x$-coordinate of a point in space. The magnitude of the electric field at a point $(-4, 0)$ is .......... $V/m$.

Similar Questions

Two large plane parallel conducting plates are kept $10 \ cm$ apart as shown in the figure. The potential difference between them is $V$. The potential difference between the points $A$ and $B$ (shown in the figure) is

The diagram below shows electric field lines in a region of space. Which of the following diagrams best shows the variation with distance $d$ of the potential $V$ along the line $XY$ as we move from $X$ to $Y$?

Let $V$ and $E$ be the potential and electric field intensity at a point,respectively. Then:

If the electric potential is given by $V = (5x^2 + 10x - 9) \ V$,what is the electric field at $x = 1 \ m$ in $V/m$?

$A$ uniform electric field having a magnitude $E_0$ and direction along the positive $X$-axis exists. If the potential $V$ is zero at $x = 0$,then its value at $x = +x$ will be:

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