A proton (mass

PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance

Problem

A proton (mass

m = 1.67\times10^{-27}\,\text{kg}

, charge

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

) moves along the x-axis in an evacuated tube. The electric potential varies only with x, according to the description below: • At

x = 0\,\text{cm}

V = 0\,\text{V}

. •

V

increases uniformly with position so that at

x = 10\,\text{cm}

V = 50\,\text{V}

. The proton is released from rest at

x = 10\,\text{cm}

and moves toward the origin. No forces other than the electrostatic force act on the proton. (a) Calculate the change in electric potential experienced by the proton as it moves from

x = 10\,\text{cm}

x = 4\,\text{cm}

. (b) Determine the magnitude of the proton’s kinetic energy when it reaches

x = 4\,\text{cm}

. (c) Find the speed of the proton at

x = 4\,\text{cm}

, expressing your answer to two significant figures. (d) Interpret physically what would happen to the proton’s motion if the potential instead decreased uniformly from

0\,\text{V}

x = 0\,\text{cm}

-50\,\text{V}

x = 10\,\text{cm}

, keeping all initial conditions the same. Provide a qualitative explanation based on energy considerations.

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