Electric Potential and Electric Potential Energy, Study notes of Physics

Download Electric Potential and Electric Potential Energy and more Study notes Physics in PDF only on Docsity! 1/27/2011 1 Electric Potential and Electric Potential Energy (cont.) What are the units of potential difference? A. Amperes B. Potentiometers C. Farads D. Volts E. Henrys What are the units of the electric field? A. V/C.  B. N/C.  C. V/m.  D. J/m2. E. Ω/m. The change in potential energy depends on the sign of a charge as well as on its magnitude. Since the force on a negative charge is opposite to the field direction, Positive charges accelerate in the direction of decreasing electric potential; Negative charges accelerate in the direction of increasing electric potential. In both cases, the charge moves to a region of lower potential energy. Exercise: A proton is fired with a speed of 200,000m/s from the midpoint of the capacitor toward the positive plate. (a)Show that this is insufficient speed to reach the positive plate (b)What is the proton’s speed as it collides with the negative plate? 1/27/2011 2 The Potential Energy of Point Charges Consider two point charges, q1 and q2, separated by a distance r Figure 20‐5 The electric potential of a point charge The charges have equal magnitude. Rank in order, from most positive to most negative, the potentials. Exercise: A charge q = 4.11x10-9C is placed at the origin, and a second charge -2q is placed at x = 1m. (a) Find the electric potential midway between the two charges. (b) Find the value of x, where the electric potential vanishes (somewhere between charges) In each case the charges are the same distance from the origin. Rank in order of increasing potential. The Electric Potential of a Charged Sphere In practice, you are more likely to work with a charged sphere, of radius R and total charge Q, than with a point charge. Outside a uniformly charged sphere, the electric potential is identical to that of a point cha ge Q at r the center. That is, 1/27/2011 5 Just as electric forces can be superposed, electric fields can as well. The Electric Flux Gauss’s Law For any closed surface enclosing total charge Qin,the net electric flux through the surface is Gauss’s law states that the electric flux through a closed surface is proportional to the charge enclosed by the surface The change in potential energy depends on the sign of a charge as well as on its magnitude. + + + - - - If a particle moves through a potential difference V, its electric potential energy changes by U = qtest V We can write the conservation of energy equations ½ mVi2 + qVi = ½ mVf2 + qVf 1/27/2011 6 Therefore, the electric potential of a point charge q (source) is: The potential created by a point charge q (source) at any distance r from the charge If more than two charges are present, the potential energy is the sum of the potential energies due to all pairs of charges: The electric potential of a group of point charges is the algebraic sum of the potentials of each charge. By SUM we mean that the potential of a given charge may be positive or negative, and SIGN is very important during the calculations of the total potential.