Electrostatic Potential and Potential Energy — Part 2: Potential energy: visual lesson, ISC Class 12 Physics

Lesson

Electrostatic potential energy

Part 2 — the energy stored in arrangements of charges, and why a dipole prefers to line up with a field.

In this lesson you will

Use U = qV for a charge in a field
Calculate the potential energy of systems of two and three point charges
Derive and use U = −p·E for a dipole in a uniform field

Concept

Potential energy of a charge in a field

A charge $q$ at a point of potential $V$ has potential energy $U = qV$ Moving it through a potential difference $\Delta V$ changes its energy by $q\Delta V$ .

The electronvolt: 1 eV = energy gained by an electron through 1 V = $1.6 \times 10^{-19}$ J.
A positive charge loses potential energy moving to lower potential (gaining kinetic energy).

Worked example

Worked example 5: accelerating an electron

An electron starts from rest and is accelerated through 100 V. Find the energy gained (in eV and J) and its final speed.

Step 1 — $\Delta K = eV = 100$ eV $= 100 \times 1.6 \times 10^{-19} = 1.6 \times 10^{-17}$ J.
Step 2 — $v = \sqrt{\dfrac{2\Delta K}{m_e}} = \sqrt{\dfrac{2 \times 1.6 \times 10^{-17}}{9.1 \times 10^{-31}}} \approx 5.93 \times 10^{6}$ m s $^{-1}$ .

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