SOLUTION: In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 3x^2y^2+ yz^3-2z^3x, where x, y,andzare measured in meters and Vis in v

Question 1166417: In a certain region, the electric potential due to a charge distribution is given by the equation V(x,y,z) = 3x^2y^2+ yz^3-2z^3x, where x, y,andzare measured in meters and Vis in volts. Calculate the magnitude of the electric field vector at the position (x,y,z) = (1.0, 1.0, 1.0).
Answer by ikleyn(52776) (Show Source): You can put this solution on YOUR website!
.


Electric field E has the components


     = ,

     = ,

     = .



So, take the partial derivatives of the potential V(x,y,z) in each direction x, y, z,

and you will get the electric field vector.



Then substitute the values  x= 1,  y= 1  and  z= 1  into these expressions, and calculate.



The vector which you get at the end, will be your answer.

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To read guiding materials, see this link
https://medium.com/@rjallain/using-the-electric-potential-to-find-the-vector-electric-field-d551df37d296

Have fun (!)

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