Question

The electric potential in a region of space as a function of position x is given by the equation V(x) = αx2 + βx - γ, where α = 2V/m2, β = 7V/m, and γ = 15V. All nonelectrical forces are negligible.

1. An electron starts at rest at x = 0 and travels to x = 20 m.

   1. Calculate the magnitude of the work done on the electron by the electric field during this process.

   2. Calculate the speed of the electron at x = 20 m.

2. Derive an equation for the x-component of the electric field as a function of position x.

3. 1. On the axes below, sketch a graph of the acceleration of the electron a as a function of position x.

   2. On the axes below, sketch a graph of the kinetic energy of the electron K as a function of position x.

4. At which of the following locations will an electron that is released from rest move in the negative x direction? Check all that apply.

   ____ x = -2 m ____x = +1 m ____x = +3 m

   Justify your answer.

5. A charged object, generating its own electric field given by E(x) = 7 V/m, is introduced in the region. What is the potential difference from x = 0 m to x = 20 m caused by the combination of the original electrical potential and the electric field of the charged object?

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Answer 1