Electric potential (A-level only) Flashcards – AQA A-level Physics (7408)

What is electric potential at a point?

Electric potential energy per unit charge at that point.

How is absolute electric potential at a point defined in terms of external work?

The work done per unit positive charge by an external agent in bringing a small test charge from infinity to the point, without changing its kinetic energy.

What is electric potential difference between two points?

The change in electric potential energy per unit charge between the points.

What is the change in electric potential energy of a charge $Q$ moved through a potential difference $\Delta V$?

$\Delta W = Q\Delta V$

When does the work done by an external agent moving a charge equal its change in electric potential energy?

When there is no change in the charge’s kinetic energy.

How is the work done by the electric field related to a charge’s change in electric potential energy?

It is the negative of the change: $W_{\text{field}} = -\Delta W$.

What is the SI unit of electric potential and potential difference, in terms of joules and coulombs?

The volt: $1\,\mathrm{V} = 1\,\mathrm{J\,C^{-1}}$.

What is an equipotential surface?

A surface with the same electric potential at every point.

What are the potential-energy change and electric-field work for a charge moving along an equipotential surface?

Both are zero: $\Delta V = 0$, so $\Delta W = Q\Delta V = 0$.

How are electric field lines oriented relative to equipotential surfaces?

They are perpendicular to the surfaces.

Why must electric field lines be perpendicular to an equipotential surface?

A field component along the surface would produce a potential change along it.

For a point charge $Q$, what are the electric potential and its magnitude at distance $r$, taking potential as zero at infinity?

$V=\frac{1}{4\pi\varepsilon_0}\frac{Q}{r}$

$|V|=\frac{1}{4\pi\varepsilon_0}\frac{|Q|}{r}$

What is the electric field strength magnitude at distance $r$ from a point charge $Q$?

$E=\frac{1}{4\pi\varepsilon_0}\frac{|Q|}{r^2}$

How does the sign of a point charge affect its signed potential and the position of its potential–distance graph?

A positive charge gives positive potential, above the axis; a negative charge gives negative potential, below the axis.

How do the graphs of potential magnitude and electric field strength against distance from a point charge compare?

$|V|$ follows an inverse-distance variation; $E$ follows an inverse-square variation. Both approach zero as distance increases, but $E$ decreases faster.

How is the signed radial electric field component related to electric potential?

$E_r = -\frac{dV}{dr}$

What does the minus sign in the electric field–potential gradient relation indicate?

The field points in the direction of decreasing potential.

How can the average electric field magnitude over a radial interval be found when the field and displacement are collinear and the potential gradient retains the same sign?

$\left|\frac{\Delta V}{\Delta r}\right|$

How is the potential change between two radial positions related to the graph of signed radial field against position?

It is the negative signed area under the graph: $\Delta V = -\int E_r\,dr$

If a radial field has a constant direction, what does the area under a field-magnitude graph give?

The magnitude of the potential difference. Its sign depends on the direction of travel relative to the field.