# How much work does the electric field do in moving a proton from a point with a potential of +125 V to a point where it is -55.0 V? Express your answer both in joules and electron volts, please.

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Given: V_a = +125 V

V_b = -55.0 V

and q_p = +1e = +1.602\times10^-19\text(C)

The electric field does work on the proton much like the gravitational field does work on a mass. A mass falls from high potential to low potential, like a positive test charge in an electric field.

`\DeltaV_(ba)=-W_(ba)/q`

which becomes `W_(ba) = -\DeltaV_(ba)*q`

`-(V_b-V_a)*q = -((-55.0V)-(125V))*(1e) = 180 eV`

To get joules, we multiply by the actual charge.

`180 eV*(1.602\times10^-19\text(J)/\text(eV))`

`=2.88\times10^(-17) \text(J)`