Question

The electric potential in a region is given by V = 5.00*x^3*y^2*z , where V is in volts, and coordinates x, y, and z are in meters. Determine the electric field at the point (2.00ˆi − 3.00ˆj − 4.00kˆ ) m .

These are my teachers requirements if you could please follow them I would really appreciate it thank you :)

In addition to being neat and clear, and actually answering the question, you must:

1) show the original principle (often in equation form)

2) substitute variables as needed


3) solve it first (before substituting numbers)

4) show every substitution (with units and correct sig figs)

5) present a boxed answer (with units and correct sig figs)

In a Force problem in more than one dimension, you MUST start with a Free Body Diagram.

Answer 1

Electric potential V = 5x^3y^3 Electric field is the negative gradient of the electric potential function the negative exists, because a positive test charge will be forced to travel to a lower electric potential, by over reasoning for defining electric potential E = -nablaV The upside down delta represents a vector of partial different ion nabla V = < partial differentionV/partial differentionx, partial different ion V/ partial different ion z > thus E = < -partial different ion V/partial different ion x, -partial: different ion V/partial different ion y, -partial: different ion V/ partial different ion z > carry out partial derivatives, remembering that other special coordinates we constants if not in the Leibniz rotation denominator E_ x = -partial different ion V/partial different ion x = -15X^2Y^2Z E_ y = -partial different ion V/ partial different ion y = -10 x^3yz E= -z = -partial different ion V/ partial different ion z = -5x^3y^2 as a vector field E < -15x^2y^2z, -10x^3yz,-5x^3y^2 > evaluating at the point