The electric potential at a place is varying | vedclass

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

Question

(C) 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

$2 \hat{i} - \hat{j} 	ext{ V m}^{-1}$

Vedclass · Answer

(C) The electric field $\vec{E}$ is related to the electric potential $V$ by the relation $\vec{E} = -
abla V = -\left( \frac{\partial V}{\partial x} \hat{i} + \frac{\partial V}{\partial y} \hat{j} ight)$.Given $V = \frac{1}{2}y^2 - 2x$.Calculating the partial derivatives:$\frac{\partial V}{\partial x} = \frac{\partial}{\partial x} (\frac{1}{2}y^2 - 2x) = -2$.$\frac{\partial V}{\partial y} = \frac{\partial}{\partial y} (\frac{1}{2}y^2 - 2x) = y$.Thus,$\vec{E} = -(-2 \hat{i} + y \hat{j}) = 2 \hat{i} - y \hat{j}$.At the point $(x = 1 	ext{ m}, y = 1 	ext{ m})$:$\vec{E} = 2 \hat{i} - (1) \hat{j} = 2 \hat{i} - \hat{j} 	ext{ V m}^{-1}$.

The electric potential at a place is varying as $V = \frac{1}{2}(y^2 - 4x) \text{ V}$. Then the electric field at $x = 1 \text{ m}$ and $y = 1 \text{ m}$ is

Similar Questions

Electric potential at any point is $V = -5x + 3y + \sqrt{15} z$,then the magnitude of the electric field is

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

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 electric potential $V$ is given as a function of distance $x$ (metre) by $V = (5x^2 + 10x - 9) \text{ V}$. The value of the electric field at $x = 1 \text{ m}$ is ...... $V/m$.

The electric potential in some region is expressed by $V = 6x - 8xy^2 - 8y + 6yz - 4z^2 \text{ volt}$. The magnitude of the electric force acting on a charge of $2 \text{ C}$ situated at the origin will be $-$ (in $\text{ N}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module