Question

What is the magnitude of the electric field at the point if the electric potential in the region is given by V 2.00xyz2, where V is in volts and coordinates x, y, and z are in meters?

Answer 1

Answer:

Electric field at a point ( x , y , z) is $E=-2yz^2-2xz^2-4xyz$ .

Explanation:

Given :

Electric potential in the region is , $V = 2xyz^2\ .$

We need to find the electric field .

We know , electric field , $E=-\dfrac{dV}{dr}$  { Here r is distance }

In coordinate system ,

$E=-\dfrac{dV}{\delta x }-\dfrac{dV}{\delta y }-\dfrac{dV}{\delta z }$  { $\delta$ is partial derivative }

Putting all values we get ,

$E=-\dfrac{2xyz^2}{\delta x }-\dfrac{2xyz^2}{\delta y }-\dfrac{2xyz^2}{\delta z }\\\\E=-2yz^2-2xz^2-4xyz$

Hence , this is the required solution.