(A) The electric field $E$ is related to the potential $V$ by the relation $E = -\frac{dV}{dx}$.Given $V = 4x^2$.Calculating the derivative: $E = -\fr

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(A) The electric field $E$ is related to the potential $V$ by the relation $E = -\frac{dV}{dx}$.Given $V = 4x^2$.Calculating the derivative: $E = -\frac{d}{dx}(4x^2) = -8x$.At the point $(1 \ m, 0, 2 \ m)$,the $x$-coordinate is $1 \ m$.Substituting $x = 1$ into the expression for $E$: $E = -8(1) = -8 \ V/m$.The negative sign indicates that the electric field is directed along the negative $X$-axis.Therefore,the magnitude is $8 \ V/m$ along the $-X$-axis.

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

Medium

The electric potential is given by $V = 4x^2 \ V$. What is the electric field at the point $(1 \ m, 0, 2 \ m)$?

A
$8 \ V/m$ along $-X$-axis
B
$8 \ V/m$ along $+X$-axis
C
$16 \ V/m$ along $-X$-axis
D
$16 \ V/m$ along $+Z$-axis

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Class 12

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Electric Potential and Capacitance

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Relation between Electric Field and Potential and Potential Gradient

Electric potential is given by $V = 6x - 8xy^2 - 8y + 6yz - 4z^2$. Then,the electric force acting on a $2 \, C$ point charge placed at the origin will be......$N$.

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The variation of potential $V$ with distance $x$ from a fixed point is as shown in the figure. The electric field at $x = 13\,m$ is......$V/m$.

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If the electric potential in a region is given by $V = 4x^2$ volts,then the electric field at the point $(1, 0, 2) \ m$ is:

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$A$ uniform electric field of $20\, N/C$ exists along the $x$-axis in a space. The potential difference $(V_B - V_A)$ for the points $A(4\,m, 2\,m)$ and $B(6\,m, 5\,m)$ is.....$V$.

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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 $V/m$?

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The electric potential is given by $V = 4x^2 \ V$. What is the electric field at the point $(1 \ m, 0, 2 \ m)$?

Similar Questions

Electric potential is given by $V = 6x - 8xy^2 - 8y + 6yz - 4z^2$. Then,the electric force acting on a $2 \, C$ point charge placed at the origin will be......$N$.

The variation of potential $V$ with distance $x$ from a fixed point is as shown in the figure. The electric field at $x = 13\,m$ is......$V/m$.

If the electric potential in a region is given by $V = 4x^2$ volts,then the electric field at the point $(1, 0, 2) \ m$ is:

$A$ uniform electric field of $20\, N/C$ exists along the $x$-axis in a space. The potential difference $(V_B - V_A)$ for the points $A(4\,m, 2\,m)$ and $B(6\,m, 5\,m)$ is.....$V$.

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

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