Electric Potential
Recall Gravitational Potential Energy How can you increase the gravitational potential energy of an object? Raise it above the surface of the earth. The amount of work done against earth s gravitational field to raise the object is equal to the increase of the gravitational potential energy of the object.
Similar things occur with electric potential Consider a large negative charge and a small positive test charge + - What happens when we move the positive charge away from the negative charge? We have to do work against the negative charge. The work done is equal to the increase in the electric potential energy of the positive charge.
Electric Potential Energy Definition: The Electric Potential Energy of a charge is equal to the work done in moving the charge against the electric field Electric Potential Energy = E e E e = W (work) What unit is work measured in? Joules (J)
Example: Which way do we move q to increase its E e A) B) C) Here we do work against the attraction force In both of these we do work against the repulsive force - q + q - q + + -
Equipotential Lines Similar to contour lines on a map In locations where the lines are closer there is a greater change in potential energy over a distance (Steeper hill) Each line represents the same amount of PE wrt sea level.
Electric Equipotential lines These lines represents regions in an electric field where a charged object will have the same E e with respect to the field. Consider a large charge Q + and a small test charge q +. Where would q + have to be placed so that there is no electrical force acting on it because of Q +? At infinity. This is considered the zero reference level for the electric field around Q + Like Sea level for gravity
As we bring q + closer to Q + we must do work against the electric field. WHY? Because of the Repulsive Forces between the like charges. Suppose as well that we can approach Q + from any direction. When we do a certain amount of work (say 10 J) we place an X.
We continue in all directions X X X X + Q + X X X X The combination of all of these Xs represents a equipotential line of 10 J
40 J The next equipotential line would be drawn at the next multiple of 10J (20J) and so on + Q + 20 J 10 J Why are the equipotential lines getting closer together as you approach the charge? There is a stronger electric field closer to the charge, which means you have to move the charge a small distance to do the same amount of work
Notes: The density of the equipotential lines indicates the strength of the electric field Equipotential lines are perpendicular to electric field lines and indicate areas where the electric potential is the same. Equipotential surfaces are the same as the lines, except in 3-dimensions. Think of the lines as a cross section of an onion and the surfaces are like the layers of the onion.
Draw the equipotential lines (at least 2) around the following: (See Page 549) 10 J 20 J + The lines are closer here because the electric field is stronger at the pointy ends
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Which has the largest amount of charge? + +
Which region has the largest electric field? B. The lines are closer A D + C B Note: D would be the area of the smallest electric field
Draw equipotential lines to show a stronger electric field at A if the object has a negative charge and weakest field is at C. A D - C B
Definition: Electric Potential Electric Potential is defined as the electric potential energy E e (W) per unit charge as the charge is moved against an electric field. Units?? V E e q Joules Coulomb Volt J C V
Example: Consider a negatively charge object. A) Where would a positive test charge be placed such that it has no electric potential energy? On the surface
B) Suppose we move the test charge (2.0 mc) away from the charged object until we do 10 J of work. i) What is the electric potential energy at this point? E e = 10 J ii) What is the electric potential at this point? E V e 10J 6 q 2.0 10 C
NOTE: There are 2 differences between electric potential and electric potential energy Electric Potential is: 1. electric potential energy per unit charge 2. always with reference to a zero level of potential. while electric potential energy is the TOTAL energy of the charge
Put Symbolically: Electric Potential V E q W q e Zero reference Electric Potential Energy Ee W
Electric Potential Difference (V) Electric Potential Difference is the energy (or work done) per unit charge to move that charge from any point of low potential to any other point of higher potential. This is similar to electric potential except it does not use a zero reference level In circuits, electric potential difference is usually shortened to potential difference or voltage.
Electric Potential Difference can be either: A rise where a charge is moved from a lower potential to a higher one. The charge gains energy. A drop where a charge is moved from a higher potential to a lower one. The charge loses energy.
Lets consider a simple circuit. Electrons gain energy in the cell. The chemical reaction provides energy to the electrons. Voltage Rise Which way does electricity flow? Electron flow, from ve to +ve Electrons lose energy in the light bulb. The energy is given off as: Light Heat Vibration Voltage Drop
Example: Hopefully this will illustrate the difference between : 6 J D 4 J C 2 J B 0 J A - Position D C B A Electric Potential Energy Electric Potential 6 J 3 V 4 J 2 V 2 J 1 V + 2C 0 J 0 V Electric Potential Difference 2 V Drop 1 V Rise 1 V Drop 3 V Rise 2 V Drop
Assignment Worksheet Sample Problems