The electric potential in a region is represe | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The electric field $\vec{E}$ is related to the electric potential $V$ by the relation $\vec{E} = -
abla V = -\left( \frac{\partial V}{\partial x}

Vedclass · Accepted Answer

$-2\hat{i} - 3\hat{j} + \hat{k}$

Vedclass · Answer

(B) The electric field $\vec{E}$ is related to the electric potential $V$ by the relation $\vec{E} = -
abla V = -\left( \frac{\partial V}{\partial x} \hat{i} + \frac{\partial V}{\partial y} \hat{j} + \frac{\partial V}{\partial z} \hat{k} ight)$.Given $V = 2x + 3y - z$,we calculate the partial derivatives:$\frac{\partial V}{\partial x} = \frac{\partial}{\partial x}(2x + 3y - z) = 2$$\frac{\partial V}{\partial y} = \frac{\partial}{\partial y}(2x + 3y - z) = 3$$\frac{\partial V}{\partial z} = \frac{\partial}{\partial z}(2x + 3y - z) = -1$Substituting these values into the expression for $\vec{E}$:$\vec{E} = -(2\hat{i} + 3\hat{j} - 1\hat{k})$$\vec{E} = -2\hat{i} - 3\hat{j} + \hat{k}$

The electric potential in a region is represented as $V = 2x + 3y - z$. The expression for the electric field strength is:

Similar Questions

Variation in electric potential is maximum if one goes

If the electric potential at any point $(x, y, z) \, m$ in space is given by $V = 3x^2$ volt,the electric field at the point $(1, 0, 3) \, m$ will be ............

An electric field $\vec{E} = (25 \hat{i} + 30 \hat{j}) \, NC^{-1}$ exists in a region of space. If the potential at the origin is taken to be zero,then the potential at $x = 2 \, m, y = 2 \, m$ is ...... $volt$.

The variation of electric potential $V$ with distance $x$ from a fixed point is shown in the figure. What is the value of the electric field at $x = 2 \ m$?

The electrostatic potential inside a charged spherical ball is given by $V = b - ar^2$,where $r$ is the distance from the centre; $a$ and $b$ are constants. Then,the charge density inside the ball is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module