Q.Do free electrons travel to region of higher potential or lower potential?

Concept: Electric Potential — a free electron, being negatively charged, moves opposite to the direction of the electric field, i.e., from lower to higher electric potential.

Reasoning:

1. The electric field $\vec{E}$ points from higher potential to lower potential (by definition, $E = -\frac{dV}{dr}$).
2. A free electron (charge $-e$) experiences a force $\vec{F} = -e\vec{E}$, opposite to $\vec{E}$. …

Why the answer isn’t obvious at first glance

The confusion here is classic. In everyday language, “potential” sounds like “opportunity” — so you might think electrons want to go where there’s more potential. But in physics, electric potential is defined in terms of the work done on a positive test charge. That definition flips everything for negative charges.

Let’s build the intuition from the ground up.

1. What electric potential actually means

Electric potential $V$ at a point is the potential energy per unit positive charge placed there. If you put a $+1 \, \text{C}$ charge at a point with high potential, it has high electric potential energy. A positive charge wants to move from high potential to low potential — just like a ball rolls downhill from high gravitational potential to low gravitational potential.

For a positive charge $q > 0$, $U = qV$ — so higher $V$ means higher $U$, and the charge “falls” toward lower $V$.

2. But electrons are negative

An electron has charge $q = -e$, where $e = 1.6 \times 10^{-19} \, \text{C}$. Its potential energy is:

Now watch what happens:

• If $V$ is high (say $+100 \, \text{V}$), then $U = -100e$ — a low (very negative) potential energy.
• If $V$ is low (say $0 \, \text{V}$), then $U = 0$ — a higher potential energy.

So for an electron, higher potential means lower potential energy, and lower potential means higher potential energy.

3. Which way does the electron “fall”?

Nature always drives charges toward lower potential energy — that’s the direction of the electric force.

• For an electron, lower $U$ occurs where $V$ is higher (because $U = -eV$). …

Method: Determining Which Way a Free Charge Moves from Potential Information

Use this method whenever a question asks which direction a charge (positive or negative) naturally moves, given information about potential rather than field.

Steps

Step 1: Write the potential energy of the charge

For a charge $q$ sitting at a point of potential $V$, its potential energy is

Step 2: Remember charges always move to reduce potential energy

A free charge accelerates in the direction that decreases $U$ — exactly like a ball rolling downhill in a gravitational analogy.

Step 3: Work out the direction for the sign of charge in question

• For a positive charge ($q>0$), $U=qV$ increases with $V$, so lower $U$ means lower $V$ — positive charges move toward lower potential. …