The electric potential in a certain region is given by the equation V(x,y,z) = 3

Question

The electric potential in a certain region is given by the equation V(x,y,z) = 3ax2y3 - 2bx2y4z2 where the potential is in volts when the positions are given in meters. The constants in this equation are given below.

Randomized Variables
a = 3.4 V/m5
b = 1.07 V/m8

Calculate the magnitude of the electric field at the point (x1,y1,z1) = (-5.0, 2.0, 1.5) m in units of newtons per coulomb.

Note: The answer E = 6937

I tried to solve this by finding the components of x, y, and z of the electric field (the following three equations are all correct):

Ex = - 6 a x y3 + 4 b x y4 z2

Ey = - 9 a x2 y2 + 8 b x2 y3 z2

Ez = 4 b x2 y4 z

Explanation / Answer

at x1 = -5 m,y1 = 2m and z1 = 1.5 m

tehn Ex = (6*3.4*5*2*2*2) -(4*1.07*5*2*2*2*2*1.5*1.5) = 45.6 V/m

Ey = (9*3.4*25*4)-(8*1.07*25*8*1.5*1.5) = 792 V/m

Ez = 4*1.07*25*2*2*2*2*1.5 = 2568 V/m

then magnitude of E is E = sqrt(Ex^2+Ey^2+Ez^2) = sqrt(45.6^2+792^2+2568^2) = 2687N/C is the correct answer

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