29: Problem 29.15

INTRO: The electric potential along the x-axis is V=100e^−2x/m V, where x is in meters.

PART A: What is E_x at x=1.0m?
Express your answer as an integer and include the appropriate units.

SOLUTION: 
E = -dV(x)/dx, the derivative of V is - 100e^−2x/m⋅(-2) V/m = 200e^−2x/m V/m
E(1) = 200e⁻² V/m = 27.067 V/m ≈ 27 V/m

PART B: What is E(x) at x=1.6m?
Express your answer to two significant figures and include the appropriate units.

SOLUTION: 
E = -dV(x)/dx, the derivative of V is - 100e^−2x/m⋅(-2) V/m = 200e^−2x/m V/m
E(1.6) = 200e^−2⋅1.6 V/m = 200e^−3.2 V/m = 8.2 V/m