Electric Potential Energy and Potential Difference

Review of Work and Energy Work = A transfer of Energy When work is done, there is a change in PE Energy = The ability to do work Work Equation The force must be parallel to do work. Work and Energy Equation Positive “+” work = the force helps the motion of the object or KE is transferred TO the object or the object is losing PE Negative “-” work = the force is trying to oppose the motion of the object or KE is being transferred FROM the object. Or the object is gaining PE © 2014 Pearson Education, Inc.

Work Done by a Uniform Electric Field Θ = the angle between F and d q is (+ or -) E = magnitude only Θ = the angle between E and d © 2014 Pearson Education, Inc.

Electric Potential Energy Negative Charges In the opposite direction of the E-Field Positive Charges In the same direction as the E- field © 2014 Pearson Education, Inc.

Electric Potential Energy Work Done By Gravity (+, cos 0) = 0 © 2014 Pearson Education, Inc.

Electric Potential Energy Work Done By Electric Force (CONSERVATIVE force) Change in electric potential energy is negative of work done by electric force:

Examples A proton moves from x=0 m to x=2.4 m in an electric field of 5000N/C pointing to the right. What is the work done by the electric field? What is the work done if the particle starts at (0,0) and ends at (3,4)? What is the work done if the particle if the first question was an electron? What is the change in electrical potential energy of question 1 and 3? © 2014 Pearson Education, Inc.

Electric Potential Energy Electrical Potential Energy The work done by an outside agent to bring 2 charges together from infinity = the change in electrical potential energy Example: How much work must be done to bring 2 charges from infinity to a distance of 5cm? © 2014 Pearson Education, Inc.

How much work must an outside agent do to bring 3 charges together as shown. © 2014 Pearson Education, Inc.

The Electron Volt, a Unit of Energy One electron volt (eV) is the energy gained by an electron moving through a potential difference of one volt. © 2014 Pearson Education, Inc.

Electric Potential Energy and Potential Difference Electric potential is defined as potential energy per unit charge; analogous to definition of electric field as force per unit charge: Unit: the volt (V). 1 V = 1 J/C. Change in potential between 2 points (A and B) POTENTIAL DIFFERENCE © 2014 Pearson Education, Inc.

Electric Potential Energy and Electric Potential Electric Potential is a scalar just like GPE It will be either positive or negative The “sign” determines value not direction. “High” potential is a larger number (more +) than a “Low” potential A positive charge has “higher” potential than a negative charge Positive charges move from High Potential to Low Potential Negative charges move from Low Potential to High Potential © 2014 Pearson Education, Inc.

Electric Potential and Work The change in Electric Potential Energy Work done by an Electric Force Work Done by an outside agent © 2014 Pearson Education, Inc.

Examples What is the electric potential 1cm away from a 1nC charge? What is the potential difference between that point and another at 3cm away from the charge? If an electron was placed at 3cm, what would happen to it? What is the speed of the electron when it gets to 1cm? © 2014 Pearson Education, Inc.

Examples Calculate the electric potential due to a collection of charges at point p. q1=5μC and q2=-2μC What is the work done to bring a 3rd point charge of 4μC from infinity to point p? © 2014 Pearson Education, Inc.

Relation between Electric Potential and Electric Field Parallel Plates Units: V = volts d = m E = N/C or V/m The (-) = the E-field points in the direction of decreasing potential © 2014 Pearson Education, Inc.

Example A pair of oppositely charged, parallel plates are separated by 5.33 mm. A potential difference of 600 V exists between the plates. (a) What is the magnitude of the electric field strength between the plates? (b) What is the magnitude of the force on an electron between the plates?

Example A pair of oppositely charged, parallel plates are separated by 5.33 mm. A potential difference of 600 V exists between the plates. (a) What is the magnitude of the electric field strength between the plates? (b) What is the magnitude of the force on an electron between the plates? 113,207.55 N/C 1.81x10-14 N

Calculate the speed of a proton that is accelerated from rest through a potential difference of 120 V

Example Calculate the speed of a proton that is accelerated from rest through a potential difference of 120 V 1.52x105 m/s

So let’s say you had a positive charge So let’s say you had a positive charge. The electric field lines move AWAY from the charge. The equipotential lines are perpendicular to the electric field lines and thus make concentric circles around the charge. As you move AWAY from a positive charge the potential decreases. So V1>V2>V3. Now that we have the direction or visual aspect of the equipotential line understood the question is how can we determine the potential at a certain distance away from the charge? r V(r) = ? Equipotential Lines

Measuring Capacitance Let’s go back to thinking about plates! Surface Charge Density C/m2 The unit for capacitance is the FARAD, F.

Energy of a Capacitor

Example A parallel plate has an area of 0.0002m2 and a plate separation of 0.001m and connected to a battery of 3V. What is the capacitance? charge on the positive plate? surface charge density? Magnitude of the electric field?

Example A 2.5x10-5F plate holds 1.75x10-3C of charge. What is the Stored energy on the plate? voltage across the plate? new voltage by doubling the stored energy of the plate?