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An equipotential surface is a surface on which the electric potential is the same everywhere. Since the potential at a distance r from an isolated point.

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Presentation on theme: "An equipotential surface is a surface on which the electric potential is the same everywhere. Since the potential at a distance r from an isolated point."— Presentation transcript:

1 An equipotential surface is a surface on which the electric potential is the same everywhere. Since the potential at a distance r from an isolated point charge is V = kq/r, the potential is the same wherever r is the same.

2 The net electric force does no work as a charge moves on an equipotential surface. The net electric force does do work as a charge moves between equipotential surfaces.

3 The electric field created by any group of charges (or a single charge) is everywhere perpendicular to the associated equipotential surfaces and points in the direction of decreasing potential.

4 The surface of any conductor is an equipotential surface when at equilibrium under electrostatic conditions.

5 Actually, since the electric field is zero everywhere inside a conductor whose charges are in equilibrium, the entire conductor can be regarded as an equipotential volume.

6 When a charge is moved between the plates of a parallel plate capacitor, the force applied is the product of the charge and the electric field F = q 0 E. The work done is W = F∆s = q 0 E∆s.

7 From previous equations: ∆V = -W/q 0 = -q 0 E∆s/q 0 or ∆V = -E∆s or E = -∆V/∆s (The magnitude of E = V/d) The quantity ∆V/∆s is called the potential gradient.

8 Ex. 9 - The plates of a capacitor are separated by a distance of 0.032 m, and the potential difference between them is ∆V = V B - V A = -64V. Two equipotential surfaces between the plates have a potential difference of -3.0 V. Find the spacing between the two equipotential surfaces.

9 A capacitor is composed of any two conductors of any shape placed near each other without touching. The region between the conductors is often filled with a material called a dielectric. A capacitor stores electric charge.

10 The proportion of charge to voltage in a capacitor is expressed with a proportionality constant called the capacitance C of the capacitor. q = CV The unit of capacitance is the coulomb/volt = farad (F).

11 One farad, one coulomb/volt is a huge capacitance. Usually smaller amounts are used in circuits (microfarad, 1µF =10 -6 F) (picofarad, pF = 10 -12 F).

12 Capacitance describes the ability of a capacity to store charge. RAM chips contain millions of capacitors. A charged capacitor is a “1”, an uncharged capacitor is a “0” in the binary system.

13 A dielectric causes the electric field between the plates to decrease. This reduction is described by the dielectric constant κ, the ratio of the electric field strength E 0 without the dielectric to the strength E inside the dielectric: κ = E 0 /E. (unitless)

14 E = E 0 /k = V/d Remember E 0 = q/(ε 0 A), (CH 18) so, q/(κε 0 A) = V/d Solving for q, gives: q = (κε 0 A/d)V, but q = VC, so: capacitance C = κε 0 A/d.

15 If C 0 is the capacitance of an empty capacitor, the capacitance of a capacitor with a dielectric is C = κ C 0. Since all dielectrics (except a vacuum) have a κ that is greater than 1; the purpose of a dielectric is to raise the capacitance.

16 Ex. 10 - The capacitance of an empty capacitor is 1.2 µF. The capacitor is connected to a 12-V battery and charged up. With the capacitor connected to the battery, a slab of dielectric material is inserted between the plates. As a result, 2.6 x 10 -5 C of additional charge flows from one plate, through the battery, and on to the other plate. What is the dielectric constant κ of the material?

17 A capacitor is a device for storing charge, but also energy. The total work done by a battery in charging a capacitor is 1/2 qV. This is stored in the capacitor as electrical potential energy, EPE = 1/2 qV. q = CV, so energy = 1/2 CVV = 1/2 CV 2.

18 But V = Ed, and C = κε 0 A/d, so: Energy = 1/2 (κε 0 A/d)(Ed) 2. A x d = the volume between the plates, so: Energy density = energy/volume = 1/2 κε 0 E 2. This is valid for any electric field strength, not just between the plates of a capacitor.

19 Capacitors are used to build up a large charge with a high potential which can then be released when needed. Capacitors such as this are used in electronic flashes in cameras, tazers and in defibrillators.

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