This video is about potential energy. Let's begin with electric potential energy.
One way to define electric potential energy is that it is the energy possessed by a charge
due to its position in an electric field. Let's recall the definition of electric potential
at a point. It is the work done per unit charge when moving a positive test charge from infinity
to this point. I put the words positive test in parentheses here because in the definition
of electric potential we refer to a positive test charge however when any charge is moved from
infinity to a point in an electric field it will have electric potential. We can express this
definition using the following equation ve is equal to w divided by q. Here ve is electric potential
w is the work done and q is the charge that was moved from infinity to the given point in the
electric field. So to summarize what we discussed so far we can say that when a charge is in an
electric field it has electric potential and because of this it has electric potential energy.
This electric potential energy is equal to the work done when moving the charge from infinity
to the point. In the previous video we learned a different equation for electric potential.
It was that ve is equal to k times uppercase q divided by r. k is the Coulomb constant,
uppercase q is the charge due to which the electric field arises and r is the distance
from this charge. It is important to understand the difference between uppercase q and lower
case q in these equations. As we said uppercase q is the charge due to which the electric field
arises and lowercase q is the charge that we place at a point in this electric field. Of course
there is also an electric field that arises due to lowercase q but what we are focusing on here
is the effect of the electric field due to uppercase q on lowercase q.
Since we have two different expressions for the electric potential we can equate kq over r
to w over q. Since we said that w the work done is equal to the potential energy
I will replace w by ep potential energy and this is divided by q.
Rearranging this equation we get the formula that is given in the ib physics data booklet.
Of course the middle term in the formula q times ve is given by rearranging the first equation
and replacing w by ep. Here are the variables that are present in this formula.
Deriving the equation for gravitational potential energy is very similar. We'll start with a
definition of gravitational potential energy which is the energy possessed by a mass due to its
position in a gravitational field. Next let's recall the definition of gravitational potential
from subtopic 10.1 which is the work done per unit mass when moving a test mass from infinity
to a point. We can write this definition as vg is equal to w over m where just as in our first
equation for electric potential w is equal to the potential energy. The alternative equation
we learned for gravitational potential in the previous video is vg is equal to negative g
times uppercase m over r. The distinction here between uppercase m and lowercase m
is similar to what it was for uppercase q and lowercase q for electric potential and electric
potential energy. Uppercase m is the mass due to which the gravitational field arises
and lowercase m is the mass that is moved to a point in this gravitational field.
Equating our two expressions for vg and replacing w by ep for potential energy,
we get that negative g uppercase m over r is equal to ep divided by lowercase m.
Rearranging gives us the formula that is in the IB physics data booklet. Here are the variables
that are present in this formula. An important point to keep in mind here that we will return
to when we learn about the total energy of an object in orbit is that gravitational potential
energy is always negative. This completes our discussion of potential energy. In the next video
we'll learn about the field and the potential inside the sphere.