Variable Potential Part A The potential as a function of position in a region is

Question

Variable Potential Part A The potential as a function of position in a region is V(x) 4x - 5x2 -x3, with x in meters and V in volts. Find all points on the x-axis (in m) where V 0. Enter your answers below separated by a comma. (You do not need to enter any units.) Submit Answer Tries 0/15 Part B Find an expression for the electric field. Submit Answer Tries 0/15 Part C Find all points on the x-axis (in m) where E = 0, Enter your answers below separated by a comma. (You do not need to enter any units) Submit Answer Tries 0/15

Explanation / Answer

A) V = 4x - 5x^2 - x^3

x^3 + 5x^2 - 4x = 0

x(x^2 + 5x - 4) = 0

x= 0 or x = -5 +- sqrt(25 + 4*4) / 2

x = 0 , x =0.7 , -5.7

B)E = -dV/dx

= - d(4x - 5x^2 - x^3) / dx

= 3x^2 + 10x - 4

C) points where E = 0

3x^2 + 10x - 4 = 0

x = -10 +-sqrt(100 + 4*4*3) / 6

x = 0.36 , -3.7

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