The electric potential in an electric field is given by V(x, y, z) = (-9.40 V/m^

Question

The electric potential in an electric field is given by V(x, y, z) = (-9.40 V/m^5) x^3 y^2 + (3.85 V/m^4) y^4 - (9.8 V/m^2)zy. Determine the unit vector form E = [E_x V/m)i + (E_y V/m)j + (E_z V/m)k] of the electric field at the point whose coordinates are (-1.3 m. 2.3 m. 3.1 m). Give the x, y, z components of electric field in the form "+/-abc" V/m, or, "ab.c" V/m as is appropriate. For example, if you calculate the electric field as E = -690 V/m i + 278 V/m j - 83.5 V/m k, then your answer should be entered as -690, +278. -83.5 Answer: _______

Explanation / Answer

We know that
E =- dV/dr
that means
EX = -dV/dx = -(d/dx)*(-9.4X3y2 + 3.85 y4 -9.8zy)
EX = - (-9.4*(3x2)*y2 + 0 - 0) = 28.2(xy)2
for x = -1.3 , y = 2.3 , z = 3.1
EX = 252.11 V/m
Similarly EY = -(d/dy)*(-9.4X3y2 + 3.85 y4 -9.8zy)
  = -(-9.4X3*(2y) + 3.85*(4y3) -9.8z)
Putting the value of x , y and z in the above equation
EY = - (94.9983 + 187.372 - (30.38)) = -251.99 V/m
Now
EZ = -(d/dz)*(-9.4X3y2 + 3.85 y4 -9.8zy)
EZ = - (0 + 0 - 9.8y) = 22.54 V/m
E = 252.11 i - 251.99 j + 22.54 k

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