Electrostatic Energy and Capacitance

1. Electrostatic Energy and Capacitance Electrostatic Potential Energy Capacitance. Capacitors Parallel-Plate Capacitor The Storage of Electrical Energy Electrostatic Field Energy Capacitors. Series and parallel Combination Dielectrics Energy stored Molecular View of a Dielectric

2. For a set of n single point charges For a set of n conductors with the ith conductor at potential Vi and charge Qi Calculate the total work required to place the point charges at each corner of the square by separately calculating the work required to move each charge to its final position. Show that the previous equation gives the total required work. Apply to the case: q= 10 µC; a= 10 cm.

3. Capacitance, Capacitors Capacitance of an isolated conductor Find the radius of a spherical conductor that has a capacitance of 220 µF Capacitance is a measure of the capacity to store charge for a given potential difference farad [F] Capacitors: A device consisting of two conductors carrying equal but opposite charges Parallel-Plate Capacitors

4. A parallel-plate capacitor has square plates of a length of 10 cm separated by 1 mm. (a) Calculate the capacitance (b) If this capacitor is charged to 12 V, how much charge is transferred from one plate to another Find an expression for the capacitance of a cylindrical capacitor consisting of two conductors, each of length L. Apply to the case: R1=.1 cm; R2= 1.2cm; L =50 cm. To represent the capacitance against the quotient R2/R1 A coaxial cable is a long cylindrical capacitor …

6. A variable air-gap capacitor (for tuning circuits of old radios) . The semicircular plates rotate through the fixed plates, which changes the amount of surface area between the plates, and hence the capacitance

7. Capacitance switching in computer keyboards. A metal plate attached to each key acts as the top plate of a capacitor. Depressing the key decreases the separation between the top and bottom plates and increases capacitance, which triggers the electronic circuitry of the compute to acknowledge the keystroke Some types of capacitors: Air - Often used in radio tuning circuits Mylar - Most commonly used for timer circuits like clocks, alarms and counters Glass - Good for high voltage applications Ceramic - Used for high frequency purposes like antennas, X-ray and magnetic resonance imaging (MRI) machines Super capacitor - Powers electric and hybrid cars In a way, a capacitor is a little like a battery. Although they work in completely different ways, capacitors and batteries both store electrical energy

8. The storage of electrical energy Work done bythebatterytochargethe capacitor QV To consider the previous square parallel-plates capacitor connected to a 12 V battery How much energy is stored in the capacitor? .How much work is done by the battery to charge the capacitor?. The battery is then disconnected and the plate separation is then increased to 3 mm. How much the stored energy now is?. To calculate the work required to separate the plates. Energydensity (energy-per-unitvolume) in anelectricfieldstrength E

9. Capacitors connected in parallel Once the switch is closed , the capacitors charge. When the capacitors are fully charged (a) what is the potential of each conductor in the circuit? (b) What is the charge on each capacitor plate? (c) What total charge passed through a battery? Equivalent Capacitance: the capacitance of a single capacitor that is operationally equivalent to the combination What is the equivalent capacitance of the above described combination?

10. Capacitors connected in series Once the switch is closed , the capacitors charge. When the capacitors are fully charged (a) what is the potential of each conductor in the circuit? (b) What is the charge on each capacitor plate? (c) What total charge passed through a battery? What is the equivalent capacitance of the above described combination? Find the equivalent capacitance of the network of three capacitors shown in the figure. (b) The are initially uncharged . Find the charge on each capacitor and the voltage drop across it if the combination is connected to a 6-V battery.

11. Storing electric energy by a capacitors combination The figure shows the so-called “capacitance bridge”. The capacitors are initially uncharged. Find the relation between the four capacitances to obtain zero potential difference between points c and d when a voltage V is applied between a and b

12. Dielectrics A no conducting material (air, paper, wood, glass,…) is called a dielectric When the space between the two conductors of a capacitor is occupied by a dielectric , the capacitances is increased by a factor κ, that is characteristic of the dielectric. It was discovered by Faraday A.- An isolated, charged capacitor Permitivity of the dielectric

13. Dielectrics A no conducting material (air, paper, wood, glass,…) is called a dielectric When the space between the two conductors of a capacitor is occupied by a dielectric , the capacitances is increased by a factor κ, that is characteristic of the dielectric. It was discovered by Faraday B.- Dielectric inserted while the battery remains connected, the battery pumps additional charge to maintain the original potential difference. Permitivity of the dielectric

14. Energy stored in the presence of a Dielectric A no conducting material (air, paper, wood, glass,…) is called a dielectric When the space between the two conductors of a capacitor is occupied by a dielectric , the capacitances is increased by a factor κ, that is characteristic of the dielectric. The stored energy when a voltage V is applied is increased κ times the stored energy without dielectric for the same potential

16. A 10 µF parallel-plate capacitor, with separation between plates about 1 mm, is charged with a 12 V battery. A.- Find the charge, the electric field and the total energy stored in the capacitor B.- Once charged is disconnected from battery. Then, a dielectric slab of constant κ= 2.5 is inserted between the plates, completely filling the gap. In this case, find the charge, the electric field in the dielectric and the total energy stored in the capacitors. C.- The battery remains connected. Then the dielectric is inserted, in this case find the charge, the electric field and the total energy stored

18. Molecular View of a Dielectric Polarization of a dielectric in presence of an electric field When a dielectric is placed on a electric field, its molecules are polarized in such a way that there is a net dipole moment parallel to the field. The net effect is the creation of a surface charge on the dielectric faces near the plates. The surface charges is called a bound charge because it is bound to the molecules of dielectric and cannot move. By this way, the net electric field in the dielectric is weakened The piezoelectric effect