If V = -5x + 3y + sqrt{15}z,then find the mag | vedclass

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

Question

(D) The electric field $\vec{E}$ is given by the negative gradient of the potential $V$: $\vec{E} = -
abla V = -\left( \frac{\partial V}{\partial x}\

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(D) The electric field $\vec{E}$ is given by the negative gradient of the potential $V$: $\vec{E} = -
abla V = -\left( \frac{\partial V}{\partial x}\hat{i} + \frac{\partial V}{\partial y}\hat{j} + \frac{\partial V}{\partial z}\hat{k} ight)$.Calculating the partial derivatives:$\frac{\partial V}{\partial x} = -5$,$\frac{\partial V}{\partial y} = 3$,and $\frac{\partial V}{\partial z} = \sqrt{15}$.Substituting these into the expression for $\vec{E}$:$\vec{E} = -(-5\hat{i} + 3\hat{j} + \sqrt{15}\hat{k}) = 5\hat{i} - 3\hat{j} - \sqrt{15}\hat{k}$.The magnitude of the electric field is $|\vec{E}| = \sqrt{(5)^2 + (-3)^2 + (-\sqrt{15})^2}$.$|\vec{E}| = \sqrt{25 + 9 + 15} = \sqrt{49} = 7$ units.

If $V = -5x + 3y + \sqrt{15}z$,then find the magnitude of the electric field $E(x, y, z)$ in units.

Similar Questions

Obtain the relation between electric field and electric potential.

Write the relation between the electric field of an electric charge and electrostatic potential at any point.

Two plates are separated by a distance of $20 \, cm$. The potential difference between them is $10 \, V$. The electric field between the two plates is ...... $V m^{-1}$.

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

The electric potential $(V)$ as a function of distance $(x)$ [in meters] is given by $V = (5x^2 + 10x - 9) \, V$. The value of the electric field at $x = 1 \, m$ would be ...... $V/m$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module