An electron (mass

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Electric Force Field and Potential · Electric Force Field and Potential

Problem

An electron (mass

m_{e} = 9.11\times10^{-31}\,\text{kg}

, charge

-e = -1.60\times10^{-19}\,\text{C}

) enters a one-dimensional region along the

+x

direction with an initial speed

v_{0} = 3.0\times10^{6}\,\text{m\,s}^{-1}

. The electric potential

V(x)

in this region is described verbally as follows: •

V(x) = 0\,\text{V}

x = 0\,\text{cm}

. • From

x = 0\,\text{cm}

x = 6\,\text{cm}

V

decreases linearly to

-30\,\text{V}

. • For

x > 6\,\text{cm}

V

remains constant at

-30\,\text{V}

. Ignore all non-electrostatic forces. (a) Determine the maximum value of

x

that the electron reaches before reversing direction (i.e., the turning point). Show all steps clearly. (b) At the turning point, what are the electron’s kinetic and electric potential energies relative to their values at

x = 0\,\text{cm}

? Explain your reasoning. (c) Sketch qualitatively (no specific scale required) the electron’s kinetic energy as a function of

x

from

x = 0\,\text{cm}

x = 8\,\text{cm}

, and label key features on your sketch.

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