# Electron volt and Voltage

Voltage is the work done per unit charge. Given by:

V = W/q

Electron volt is the maximum kinetic energy gained by the electron in falling through a potential difference of 1 volt. Given by:

K.E (max) = eV

When there is a potential difference (voltage) of 10V between two points, it means that we are doing 10 joules of work per unit charge (electron).

My question is that if we are doing 10 joules of work on an electron than why isn't the kinetic energy of electron equal to 10 joules? Why do we multiply charge of electron with Voltage to get the kinetic energy gained by the electron?

• The SI unit of charge is the Coulomb, not the charge of the electron. 1 Joule = 1 Coulomb * 1 Volt, which is substantially larger than an eV because a Coulomb is substantially larger than the electron charge. :) – Michael Brown Mar 9 '13 at 0:17

Fact. When there is a potential difference $\Delta V$ between two points, then if a charge $q$ moves from one of the points to the other, then its electrostatic potential energy will change by $\Delta U = q \Delta V$.
Therefore, if an electron moves from one point to the other, and if there are no other interactions around, then the change in its electrostatic potential energy in going from one point to the other will equal the (negative of) the change in its kinetic energy by energy conservation: $$U_1 + K_1 = U_2 + K_2 \implies \Delta U = -\Delta K$$