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This video is about potential energy. Let's begin with electric potential energy.

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One way to define electric potential energy is that it is the energy possessed by a charge

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due to its position in an electric field. Let's recall the definition of electric potential

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at a point. It is the work done per unit charge when moving a positive test charge from infinity

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to this point. I put the words positive test in parentheses here because in the definition

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of electric potential we refer to a positive test charge however when any charge is moved from

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infinity to a point in an electric field it will have electric potential. We can express this

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definition using the following equation ve is equal to w divided by q. Here ve is electric potential

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w is the work done and q is the charge that was moved from infinity to the given point in the

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electric field. So to summarize what we discussed so far we can say that when a charge is in an

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electric field it has electric potential and because of this it has electric potential energy.

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This electric potential energy is equal to the work done when moving the charge from infinity

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to the point. In the previous video we learned a different equation for electric potential.

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It was that ve is equal to k times uppercase q divided by r. k is the Coulomb constant,

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uppercase q is the charge due to which the electric field arises and r is the distance

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from this charge. It is important to understand the difference between uppercase q and lower

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case q in these equations. As we said uppercase q is the charge due to which the electric field

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arises and lowercase q is the charge that we place at a point in this electric field. Of course

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there is also an electric field that arises due to lowercase q but what we are focusing on here

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is the effect of the electric field due to uppercase q on lowercase q.

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Since we have two different expressions for the electric potential we can equate kq over r

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to w over q. Since we said that w the work done is equal to the potential energy

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I will replace w by ep potential energy and this is divided by q.

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Rearranging this equation we get the formula that is given in the ib physics data booklet.

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Of course the middle term in the formula q times ve is given by rearranging the first equation

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and replacing w by ep. Here are the variables that are present in this formula.

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Deriving the equation for gravitational potential energy is very similar. We'll start with a

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definition of gravitational potential energy which is the energy possessed by a mass due to its

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position in a gravitational field. Next let's recall the definition of gravitational potential

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from subtopic 10.1 which is the work done per unit mass when moving a test mass from infinity

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to a point. We can write this definition as vg is equal to w over m where just as in our first

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equation for electric potential w is equal to the potential energy. The alternative equation

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we learned for gravitational potential in the previous video is vg is equal to negative g

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times uppercase m over r. The distinction here between uppercase m and lowercase m

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is similar to what it was for uppercase q and lowercase q for electric potential and electric

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potential energy. Uppercase m is the mass due to which the gravitational field arises

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and lowercase m is the mass that is moved to a point in this gravitational field.

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Equating our two expressions for vg and replacing w by ep for potential energy,

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we get that negative g uppercase m over r is equal to ep divided by lowercase m.

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Rearranging gives us the formula that is in the IB physics data booklet. Here are the variables

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that are present in this formula. An important point to keep in mind here that we will return

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to when we learn about the total energy of an object in orbit is that gravitational potential

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energy is always negative. This completes our discussion of potential energy. In the next video

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we'll learn about the field and the potential inside the sphere.