After Chapter 5.4, you will be able to:
Electric potential, discussed here, and electric potential energy, discussed previously, sound like the same (or nearly the same) thing. They are not, although they are very closely related. In fact, electric potential is defined as the ratio of the magnitude of a charge’s electric potential energy to the magnitude of the charge itself.
where V is the electric
potential measured in volts (V) and
Even if there is no test charge q, we can still calculate the electric
potential of a point in space in an electric
field as long as we know the magnitude of the source charge and the distance from
the source charge to the point in space in the field. By dividing
by q, we get:
Electric potential is a scalar quantity, and its sign is determined by the sign of the source charge Q. For a positive source charge, V is positive, but for a negative source charge, V is negative. For a collection of charges, the total electric potential at a point in space is the scalar sum of the electric potential due to each charge.
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These are essential equations for Test Day. Know how they relate to each other and when to use them. By memorizing Coulomb’s law, you should be able to recreate the table through mathematical manipulation. From left to right, multiply by r; from top to bottom, divide by q.
Because electric potential is inversely proportional to the distance from the source charge, a potential difference will exist between two points that are at different distances from the source charge. If Va and Vb are the electric potentials at points a and b, respectively, then the potential difference between them, known as voltage, is Vb – Va. From the equation for electric potential above, we can further define potential difference as:
where Wab is the work needed to move a test charge q through an electric field from point a to point b. The work depends only on the potentials at the two points a and b and is independent of the actual pathway taken between a and b. Like gravitational force, the electrostatic force is a conservative force.
The “plus” end of a battery is the high-potential end, and the “minus” end of a battery is the low-potential end. Positive charge moves from + to – (the definition of current) while negative charge moves from – to +.
We’ve already seen that charges, if allowed, will move spontaneously in whatever direction results in a decrease in electric potential energy. For a positive test charge, this means moving from a position of higher electric potential to a position of lower electric potential. The voltage, ΔV = Vb – Va, is negative in this case; because q is positive (for a positive test charge), thus, Wab must be negative, which represents a decrease in electric potential energy.
Electric potential is the ratio of the work done to move a test charge from infinity to a point in an electric field surrounding a source charge divided by the magnitude of the test charge.
Now let’s consider a negative test charge. A negative test charge will spontaneously move from a position of lower electric potential to a position of higher electric potential. The voltage, ΔV = Vb – Va, is positive in this case; because q is negative (for a negative test charge), Wab must also be negative, which again represents a decrease in electric potential energy. The takeaway: positive charges will spontaneously move in the direction that decreases their electric potential (negative voltage), whereas negative charges will spontaneously move in the direction that increases their electric potential (positive voltage)—yet, in both cases, the electric potential energy is decreasing.
Create analogies between mechanics and electrostatics to familiarize yourself with these concepts. Electric field is like a gravitational field, and it exerts forces on charges much like a gravitational field exerts forces on masses. A test charge has a particular electric potential energy at a given electric potential, depending on the magnitude of its charge, much like a mass has a particular gravitational potential energy, depending on the magnitude of its mass. These mechanics concepts are discussed in Chapters 1 and 2 of MCAT Physics and Math Review.