Video Transcript
Two identical rods are shown in the
following figure. Within the rods are electric
charges. Positive charges are shown in red,
and negative charges are shown in blue. All the charges have equal
magnitudes. The charges cannot move. Which rod has the greater electric
potential difference across it? (A) Rod A. (B) Rod B. Or (C) the potential difference is
the same across each rod.
To answer this question, we need to
work out which rod has the greater potential difference across its ends. Let’s first remind ourselves of the
relationship between potential difference and electric charge. We can recall that opposite charges
attract. If we place a positive charge and a
negative charge a distance apart, there will be an attractive force between them
that pulls them towards each other.
If we wanted to keep these charges
separate, we’d need to do work on the charges so they had enough energy to overcome
this attractive force. When we separate opposite charges
like this, we create an electric potential difference between them. Note that we have opposite charges
here. Opposite charges attract each
other, so work needs to be done to keep them separate. This is what leads to a potential
difference.
Like charges do not attract. In fact, they actually repel each
other. So, if we have two negative
charges, for example, we don’t need to do any work to keep them separate. This means there is no potential
difference between like charges. In short, a potential difference is
only created when opposite charges are separated. Now that we know this, we’re ready
to answer this question: which of these rods has the greater potential difference
across it?
First, let’s look at rod A. We can see that there’s a negative
charge on this side of the rod and a positive charge on this side. So, we have opposite charges that
have been separated by a distance. This means there is a potential
difference across this rod.
Next, let’s look at rod B. Rod B contains four charges: two
positive and two negative. Although we do have opposite
charges here, these opposite charges have not been separated. For example, this negative charge
is right next to both of the positive charges. This positive charge is right next
to both negative charges. Since the opposite charges have not
been separated, no work has been done on the charges, and there is zero potential
difference across the ends of this rod.
So, rod A must have a greater
potential difference across it than rod B, since rod B has no potential difference
across it at all. The correct answer to this question
is therefore option (A).
