The electric potential at any point (x, y, z) | vedclass

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Question

(D) The relation between electric field $\overrightarrow{E}$ and electric potential $V$ is given by $\overrightarrow{E} = -
abla V = -\left( \frac{\p

Vedclass · Accepted Answer

$-10\hat{i}$

Vedclass · Answer

(D) The relation between electric field $\overrightarrow{E}$ and electric potential $V$ is given by $\overrightarrow{E} = -
abla V = -\left( \frac{\partial V}{\partial x}\hat{i} + \frac{\partial V}{\partial y}\hat{j} + \frac{\partial V}{\partial z}\hat{k} ight)$.Given $V = 5x^2$.Calculating the partial derivatives:$\frac{\partial V}{\partial x} = \frac{d}{dx}(5x^2) = 10x$$\frac{\partial V}{\partial y} = 0$$\frac{\partial V}{\partial z} = 0$Thus,$\overrightarrow{E} = -(10x)\hat{i} = -10x\hat{i} 	ext{ N/C}$.At the point $(1, 2, 3) 	ext{ m}$,substituting $x = 1$:$\overrightarrow{E} = -10(1)\hat{i} = -10\hat{i} 	ext{ N/C}$.Therefore,the correct option is $D$.

The electric potential at any point $(x, y, z)$ (all in meters) in space is given by $V = 5x^2$ volt. The electric field at the point $(1, 2, 3) \text{ m}$ is $\overrightarrow{E} = $ . . . . . . $\text{N/C}$.

Similar Questions

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 $Y$?

The figure shows the electric potential $V$ as a function of distance through five regions on the $x$-axis. Which of the following is true for the electric field $E$ in these regions?

The potential at a point $x$ (measured in $\mu m$) due to some charges situated on the $x$-axis is given by $V(x) = \frac{20}{x^2 - 4} \text{ volt}$. The electric field $E$ at $x = 4 \mu m$ is given by:

The potential $\phi(x, y)$ of an electrostatic field $\vec{E} = a(y \hat{i} + x \hat{j})$ is [where $a$ is a constant and $\hat{i}$ and $\hat{j}$ are unit vectors along $X$ and $Y$ axes].

Determine the electric field strength vector if the potential of this field depends on $x, y$ coordinates as $V = 10axy$.

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