19.5 CAPACITORS AND DIELECTRICS Parallel plate capacitor consists of two parallel metal plates placed near one another but not touching. Capacitor: two conductors of any shape placed near one another without touching. Common to fill the region between the conductors or plates with an electrically insulating material called a dielectric.

Capacitor stores electric charge. Each capacitor plate carries a charge of the same magnitude, one positive and the other negative. The EP of the positive plate exceeds that of the negative plate by an amount V (because of the charge). When q is doubled so is v, proportional C proportionality constant, capacitance of the capacitor.

THE RELATION BETWEEN CHARGE AND POTENTIAL DIFFERENCE FOR A CAPACITOR The magnitude q of the charge on each plate of a capacitor is directly proportional to the magnitude V of the potential difference between the plates:

Michael Faraday Farad is an enormous capacitance. Microfarad 10^-6, picofarad 10^-12are usually used in electric circuits. The capacitance reflects the ability of the capacitor to store charge. The larger capacitance C allows more charge q to be put onto the plates for a given value of the potential difference V.

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THE DIELECTRIC CONSTANT A dielectric can alter the electric field between the plates. Ex. Water Arrange themselves end to end, attracted to the opposite charges. The left surface becomes positively charged, and the right surface becomes negatively charged. Not all electric field lines go through dielectric.

The electric field inside the dielectric is less strong than the electric field inside the empty capacitor. Dielectric constant K: reduction in the electric field, ratio of the field magnitude Eo without the dielectric to the field magnitude E inside the dielectric:

Number without units since it’s a ratio. The value of K depends on the nature of the dielectric material. Table 19.1 pg. 587

THE CAPACITANCE OF A PARALLEL PLATE CAPACITOR Capacitance of a capacitor is affected by the geometry of the plates and the dielectric constant of the material between them. A = area of plate d = separation between the plates. Magnitude of the electric field inside the dielectric is: E = V/d V = potential difference between the plates.

If the charge on each plate is kept fixed, the EF inside the dielectric is related to the EF in the absence of the dielectric

εo = 8.85 x 10^-12 C^2/Nm^2 εo = 1/4πk

q = CV (19.8) Plug in for q Only the geometry of the plates (A and d) and the dielectric constant K affect the capacitance.

Capacitors are filled with dielectric materials to increase the capacitance. Capacitance with the dielectric present is increased by a factor of K over the capacitance without the dielectric. C = KCo

EXAMPLE 10: STORING ELECTRIC CHARGE The capacitance of an empty capacitor is 1.2uF. 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^-5C of additional charge flows from one plate, through the battery, and onto the other plate. What is the dielectric constant of the material?

Practice Problem 36. An axon is the relatively long tail-like part of a neuron, or nerve cell. The outer surface of the axon membrane (dielectric constant = 5), thickness = 1 x 10^-8 m, is charged positively, and the inner portion is charged negatively. Thus, the membrane is a kind of capacitor. Assuming that an axon can be treated like a parallel plate capacitor with a plate area of 5 x 10^-6m^2, what is its capacitance?

38. What voltage is required to store 7.2 x 10^-5C of charge on the plates of a 6.0uF capacitor?

Take the last two digits of the year in which you were born -now add the age you will be this year the result will be 111

ENERGY STORAGE IN A CAPACITOR When a capacitor stores charge, it also stores energy. Battery transfers charge from one plate of the capacitor to the other plate. Work done is equal to the product of the charge increment and the potential difference between the plates. As each increment of charge is moved, the potential difference increases slightly.

A larger amount of work is needed to move the next increment. W = product of the total charge q transferred and the average potential difference V (to charge up the capacitor) W = qV Since the average potential difference is ½ the final potential V, or V = ½ V, the total work done by the battery is W = ½ qV Energy = ½ qV (the work is stored as energy)

q = CV V = q/C Energy = ½ qV (19. 11a) Energy = ½ (CV)V = ½ CV^2 (19 q = CV V = q/C Energy = ½ qV (19.11a) Energy = ½ (CV)V = ½ CV^2 (19.11b) Energy = ½ q(q/C) = q^2/2C (19.11c)

Energy can be stored in the electric field between the plates. V = Ed C = KεoA/d

Since the area A times the separation d is the volume between the plates, the energy per unit volume or energy density is

Review Game Round 1 1. Work done by the electric force as the test charge (qo = +2.0 x 10^-6 C) moves from A to B is Wab = +5.0 x 10^-5J. (a) Find the value of the difference, EPE = EPEb – EPEa, in the electric potential energies of the charge between these points. (b) Determine the potential difference, V = Vb – Va, between the points.

2. The wattage of a lightbulb is 60. 0W 2. The wattage of a lightbulb is 60.0W. Determine the number of particles, each carrying a charge of 1.60 x 10^-19C (the magnitude of the charge on an electron), that pass between the terminals of 12-V car battery when the headlight burns for one hour.

Pg.577

3. A particle has a mass of 1. 8 x 10^-5kg and a charge of +3 3. A particle has a mass of 1.8 x 10^-5kg and a charge of +3.0 x 10^-5C. It is released from rest at point A and accelerates until it reaches point B. The particle moves on a horizontal straight line and does not rotate. The only forces acting on the particle are the gravitational force and an electrostatic force. The electric potential at A is 25V greater than that at B; in other words, Va – Vb = 25V. What is the translational speed of the particle at point B?

Pg. 579

q1 = +5.0uC q2 = +6.0uC q3 = -2.0uC 4. There are three point charges; initially, they are infinitely far apart. They are then brought together and placed at the corners of an equilateral triangle one by one. Each side of the triangle has a length of 0.50m. Determine the electric potential energy of the triangular group. In other words, determine the amount by which the electric potential energy of the group differs from that of the three charges in their initial, infinitely separated locations.

3

5. The capacitance of an empty capacitor is 1. 2uF 5. The capacitance of an empty capacitor is 1.2uF. 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^-5C of additional charge flows from one plate, through the battery, and onto the other plate. What is the dielectric constant of the material?