Problem 6: The electric potential in a certain region is given by the equation V(x,y,z) = 3x²y³ - 2x²y⁴z² where the potential is in volts when the positions are given in meters.

Part (a) Write an equation for the x-component of the electric field. Expression Ex = Select from the variables below to write your expression. Note that all variables may not be required. a, B, Y, 0, d, g, h, j, k, m, P, t, X, y, Z Part (b) Write an equation for the y-component of the electric field. Expression _ Ev = Select from the variables below to write your expression. Note that all variables may not be required. a, B, y, 0, d, g, h, j, k, m, P, t, X, y, Z Part (c) Write an equation for the z-component of the electric field. Expression Ez = Select from the variables below to write your expression. Note that all variables may not be required. a, B, y, 0, d, g, h, j, k, m, P, t, x, y, Z Part (d) The constants in this equation are a = 5.3 V/m and y = 0.88 V/mo. Using this information, calculate the magnitude of the electric field at the point (xL,v1,z1) = (-5.0, 2.0, 1.5) m in units of newtons per coulomb. Numeric _: A numeric value is expected and not an expression. E