1. Electrostatics #5 Capacitance

2. Capacitance I. Define capacitance and a capacitor: Capacitance is defined as the ability of an object to store charge. A capacitor is an electronic component of circuits.

3. The simplest capacitor is one made of two ________________ metal sheets, or plates. parallel the amount of charge stored on the capacitor. The parallel plates always carry equal but opposite charges. Note: Where there is a charge separation, there is also an ____________ field. The field exists between the plates and points from _____ towards ____. electric Also, where there is an electric field, there is also an ___________ ___________. The _____ plate is the higher electric potential and the _____ plate is the lower electric potential. electric potential

4. lower electric potential higher electric potential direction of electric field

5. For a constant electric field, the change of electric potential is given by: For the capacitor, this can be simplified to This is just the magnitude of the electric potential between the two plates. The capacitance is defined through the electric potential _____ and the charge held on the plates, _____. The equation for capacitance is: next slide for definitions…

6. |  V| = the electric potential between the two plates. When charge is placed on a capacitor, an initial electric potential must be provided by a battery. Q = the electric charge stored on the capacitor C = the capacitance of the device. The greater the capacitance, the more charge stored on the device for a given voltage. The units of capacitance are given the special name of ____________ and have a symbol of ‘F’. What is the farad equivalent to? farad

8. Ex. 1: A parallel plate capacitor is made of circular metal sheets placed 0.100 mm apart and has a capacitance of 1.00  F. If air is used as the insulator between the two metal plates, what is the maximum amount of charge that may be stored on this capacitor? Air ceases to be an insulator when the electric field is larger than and

9. II. The capacitance of a parallel plate capacitor can be calculated from its dimensions: The area of the overlap of the two sheets or plates and the distance between the plates. A A = the area that the two surfaces overlap (one covers the other) d d = the distance between the plates (plate separation) The capacitance, C, is proportional to the ________ and inversely proportional to the _______________ between the plates. area distance or

10. The constant  o is called the electric permittivity of free space, and the value of  o is: The permittivity constant is related to the coulomb constant, The coulomb constant is derived from the force between charges, and the permittivity constant is derived through Gauss’ Law. The actual relation is:

11. Ex. 2: A 1.00  F capacitor is constructed with its metal plates set 0.100 mm apart. If the plates are circular in shape, what is the diameter of the plates?

12. Ex. 3 A 1.00 F capacitor is constructed with square metal plates set 1.00 mm apart. What is the length of a side for the metal plates? s = the length of one side of the square area

13. III. Energy stored in a capacitor: Since the parallel plate capacitor has two plates that are oppositely charged, there is energy stored in the electric interaction between the two plates. This energy is stored in the electric field between the two plates. The energy is: U = the electric energy stored in a capacitor. Ex. 4: A parallel plate capacitor is made with an air gap of 0.0100 mm and circular plates with a diameter of 3.25 cm. a. What is the capacitance of this capacitor?

14. b. What is the maximum charge that may be placed on this capacitor? Let E have a value of and

15. c. What is the energy stored in this capacitor? d. What is the energy density between the plates of the capacitor? u = the energy density, or energy per unit volume.

16. Note: Alternate form to energy density! You do not need to memorize this derivation…