(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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Electric Potential and Capacitance

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Relation between Electric Field and Potential and Potential Gradient

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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For a given electric field $\vec{E} = 2x\hat{i} + 3y\hat{j}$,find the potential at $(X, Y)$ if the potential at the origin is $5\, V$.

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$A$ uniform electric field of $400 \, V/m$ is directed $45^\circ$ above the $x$-axis. The potential difference $V_A - V_B$ is: (Coordinates are in cm) (in $, V$)

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If on the $x$-axis electric potential decreases uniformly from $60 \,V$ to $20 \,V$ between $x=-2 \,m$ to $x=+2 \,m$,then the magnitude of electric field at the origin

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The potential of the electric field produced by a point charge at any point $(x, y, z)$ is given by $V = 3x^2 + 5$,where $x, y$ are in metres and $V$ is in volts. The intensity of the electric field at $(-2, 1, 0)$ is

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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

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......$V/m$.

For a given electric field $\vec{E} = 2x\hat{i} + 3y\hat{j}$,find the potential at $(X, Y)$ if the potential at the origin is $5\, V$.

$A$ uniform electric field of $400 \, V/m$ is directed $45^\circ$ above the $x$-axis. The potential difference $V_A - V_B$ is: (Coordinates are in cm) (in $, V$)

If on the $x$-axis electric potential decreases uniformly from $60 \,V$ to $20 \,V$ between $x=-2 \,m$ to $x=+2 \,m$,then the magnitude of electric field at the origin

The potential of the electric field produced by a point charge at any point $(x, y, z)$ is given by $V = 3x^2 + 5$,where $x, y$ are in metres and $V$ is in volts. The intensity of the electric field at $(-2, 1, 0)$ is

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