Phys chapter 20 notes

Phys chapter 20 notes - Chapter 20: Electric Potential and...

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Chapter 20: Electric Potential and Capacitance 1. The concepts covered in this chapter are: 1. Electric potential 2. Electric potential energy 3. Capacitance 4. Capacitors arranged in series and parallel configuration 5. Air- and dielectric-filled capacitors 6. Potential energy stored in capacitors 2. Potential and Potential Energy. In the previous chapter we learned that charges exert a force on each other according to Coulomb’s law. This means that such forces that occur among the charges can change a given configuration of charges: in the field view of electrostatic interaction the electric fields of various charges interact to make the charges move, i.e., the electric field does work on the charge configuration). The configuration can also be changed by an external agent, i.e., work can be performed by an external agent. This change in charge configuration will show up as a change in the potential energy of the system (the charge configuration). The change in the potential energy between (or of ) two charges is defined as Δ W field = − Δ W ext = Δ U …[1] Δ U ab = U a –U b = . bb aa . F dr q E dr = ∫∫ JK JJ KJ J KJJK …[2] The potential difference Δ V = V b - V a is defined as: V b - V a = . b a E dr JK JJK …[3] Potential can be defined as the potential energy per unit charge ( recall a similar definition of the electric field E as the force per unit charge, q E = F ) A point charge Q, creates an electric potential V(r) at a distance r from it given by: V(r) = kQ/r ( referenced to infinity, i.e., 0 () V ∞ = ) …[4] 1
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The net potential at a given point due to a collection of charges is simply the algebraic sum of individual potentials 1 n i i i Q Vk r = = [ 5 ] Potential energy of two point charges is given by U 12 = kQ 1 Q 2 / r …[6] Potential energy of a collection or configuration of point charges is the algebraic sum of the potential energy of all the pairs of charges you can form in the configuration. For example, in Solved Example 1 below, U i is the potential energy of the 3-charge configuration. Potential energy of a single charge in a collection or configuration of point charges is the algebraic sum of the potential energy of all the pairs the given charge forms in the configuration. For example, Solved Example 1 the potential energy of Q 1 in part [a] would be the sum U 12 + U 13 . Points to remember : 1. Make sure you understand the difference between potential and potential energy, and between potential energy of a charge configuration and the potential energy of a charge in a charge configuration. 2. A single charge will create a potential at a point in space, but you need at least two charges for the potential energy to have any meaning. 3. Potential and potential energy are scalars. 4. Eq. [3] can also be expressed as : 2
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E x = - dV/dx ( and similar relations in the y- and z-directions) .This allows one to calculate the components of E (a vector) by knowing the potential V(x,y,z) which is a scalar. Please see sec. 20-4 of your Text for additional details.
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Phys chapter 20 notes - Chapter 20: Electric Potential and...

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