Answer:
Electric field at a point ( x , y , z) is [tex]E=-2yz^2-2xz^2-4xyz[/tex] .
Explanation:
Given :
Electric potential in the region is , [tex]V = 2xyz^2\ .[/tex]
We need to find the electric field .
We know , electric field , [tex]E=-\dfrac{dV}{dr}[/tex] { Here r is distance }
In coordinate system ,
[tex]E=-\dfrac{dV}{\delta x }-\dfrac{dV}{\delta y }-\dfrac{dV}{\delta z }[/tex] { [tex]\delta[/tex] is partial derivative }
Putting all values we get ,
[tex]E=-\dfrac{2xyz^2}{\delta x }-\dfrac{2xyz^2}{\delta y }-\dfrac{2xyz^2}{\delta z }\\\\E=-2yz^2-2xz^2-4xyz[/tex]
Hence , this is the required solution.
