(A) The potential gradient is defined as the potential drop per unit length,given by $E = \frac{V}{L}$.From Ohm's law,$V = iR$,where $R = \rho \frac{L

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(A) The potential gradient is defined as the potential drop per unit length,given by $E = \frac{V}{L}$.From Ohm's law,$V = iR$,where $R = \rho \frac{L}{A}$.Substituting $R$ into the potential gradient formula:$E = \frac{i \rho L}{A L} = \frac{i \rho}{A}$.Given values: $i = 0.2 \, A$,$\rho = 40 \times 10^{-8} \, \Omega \, m$,and $A = 8 \times 10^{-6} \, m^2$.Substituting these values:$E = \frac{0.2 \times 40 \times 10^{-8}}{8 \times 10^{-6}}$.$E = \frac{8 \times 10^{-8}}{8 \times 10^{-6}} = 10^{-2} \, V/m$.

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

Difficult

What is the potential gradient in a wire of resistivity $40 \times 10^{-8} \, \Omega \, m$ and cross-sectional area $8 \times 10^{-6} \, m^2$ when a current of $0.2 \, A$ flows through it?

A
$10^{-2} \, V/m$
B
$10^{-1} \, V/m$
C
$3.2 \times 10^{-2} \, V/m$
D
$1 \, V/m$

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Electric Potential and Capacitance

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Relation between Electric Field and Potential and Potential Gradient

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Medium

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DifficultAP EAMCET 2022

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Assume that an electric field $E=20 x^2 \hat{i}$ exists in space. If $V_0$ is the potential at the origin and $V_A$ is the potential at $x=3 \ m$,then the potential difference $V_A-V_0$ in volts is

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As shown in the figure, if the values of the electric potential at three points $A, B$ and $C$ in a uniform electric field $(\vec{E})$ are $V_A, V_B$, and $V_C$ respectively, then

EasyAP EAMCET 2025

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The electrostatic potential in a charged spherical region of radius $r$ varies as $V = ar^3 + b$, where $a$ and $b$ are constants. The total charge in the sphere of unit radius is $\alpha \times \pi a \epsilon_0$. The value of $\alpha$ is . . . . . . .

MediumJEE MAIN 2026

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What is the potential gradient in a wire of resistivity $40 \times 10^{-8} \, \Omega \, m$ and cross-sectional area $8 \times 10^{-6} \, m^2$ when a current of $0.2 \, A$ flows through it?

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Electric potential in a region is varying according to the relation $V = \frac{3x^2}{2} - \frac{y^2}{4}$,where $x$ and $y$ are in $m$ and $V$ is in $V$. Electric field intensity (in $N/C$) at a point $(1 \, m, 2 \, m)$ is:

In a space having electric field $\vec{E}=A(x \hat{i}+y \hat{j})$,the potential at a point $(10 \ m, 20 \ m)$ is zero. Then the potential at the origin is $\left[A=10 \ Vm^{-2}\right]$. (in $V$)

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