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

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

Step-by-step explanation:

Given :

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

We need to find the electric field .

We know , electric field ,
`E=-(dV)/(dr)` { Here r is distance }

In coordinate system ,

`E=-(dV)/(\delta x )-(dV)/(\delta y )-(dV)/(\delta z )` {
`\delta` is partial derivative }

Putting all values we get ,

`E=-(2xyz^2)/(\delta x )-(2xyz^2)/(\delta y )-(2xyz^2)/(\delta z )\\\\E=-2yz^2-2xz^2-4xyz`

Hence , this is the required solution.