ENGINEERING PHYSICS SEMESTER /2012

ENGINEERING PHYSICS Sub Topics ● Charge units ● Electric field ● Electric force & Coulomb’s Law ● Capacitance and unit ● Parallel plate capacitor ● Dielectric constant and it’s function SEMESTER /2012

ENGINEERING PHYSICS Electric Potential Energy ● To move a charge from one point to another point in E, a work need to be done ● Work done by external force to move a +ve charge (+q) from A to B in E =F/q by a charge +Q state as ● : When charge moves from UA to UB, energy changes In general, electric potential energy given by SEMESTER /2012 dr = charge displacement θ = angle between F’ and dr F’ =F by E, but in different direction +Q+q E=F/q UAUA UBUB

ENGINEERING PHYSICS Electric Potential Energy It takes work to move a charge against an electric field. Just as with gravity, this work increases the potential energy of the charge. SEMESTER /2012 SI unit : Joule

ENGINEERING PHYSICS Electric Potential Difference Just as with the electric field, it is convenient to define a quantity that is the electric potential energy per unit charge. This is called the electric potential. SEMESTER /2012 Electric potential difference SI unit of electric potential: Joule/Coulomb or the volt, V.

ENGINEERING PHYSICS Electric Potential Difference The potential difference ∆V between parallel plates can be calculated relatively easily: SEMESTER /2012 Where d is the separation between two parallel plates. For a pair of oppositely charged parallel plates, the positively charged plate is at a higher electric potential than the negatively charged one by an amount ΔV.

ENGINEERING PHYSICS Electric Potential Difference As with potential energy, only changes in the electric potential can be defined. The choice of V = 0 is arbitrary. SEMESTER /2012 ∆V is independent of reference point !!!

ENGINEERING PHYSICS Electric Potential Difference Potential differences are defined in terms of positive charges, as is the electric field. Therefore, we must account for the difference between positive and negative charges. Positive charges, when released, accelerate toward regions of lower electric potential. Negative charges, when released, accelerate toward regions of higher electric potential. SEMESTER /2012

ENGINEERING PHYSICS Example Imagine moving a proton from negative plate to the positive plate of the parallel-plate arrangement. The plates are 1.5cm apart, and the field is uniform with a magnitude of 1500 N/C. (a) What is the change in the proton’s electric potential energy? (b) What is the electric potential difference (voltage) between the plates? (c) If the proton is released from rest at the positive plate, what is the speed will it have just before it hits the negative plate? SEMESTER /2012

ENGINEERING PHYSICS Given: E = 1500 N/C ; q p = +1.6 x C ; m p = 1.67 x kg ; d = 1.5 x m SEMESTER /2012 Solution: Total energy of proton is constant ∆U is negative – when its return to negative plate a) b) c)

ENGINEERING PHYSICS Electric Potential Difference Due to a Point Charge Electric potential difference of a point charge: SEMESTER /2012

ENGINEERING PHYSICS Electric Potential Difference Due to a Point Charge Whether the electric potential increases or decreases when towards or away from a point charge depends on the sign of the charge. Electric potential increases when moving nearer to positive charges or farther from negative charges. Electric potential decreases when moving farther from positive charges or nearer to negative charges. SEMESTER /2012

ENGINEERING PHYSICS Electric Potential Energy of Various Charge Configuration The electric potential energy of a system of two charges is the change in electric potential multiplied by the charge. SEMESTER /2012 Mutual electric potential energy (two charges)

ENGINEERING PHYSICS Electric Potential Energy of Various Charge Configuration The additional potential energy due to a third charge is the sum of its potential energies relative to the first two. Further charges extend the sum. SEMESTER /2012

ENGINEERING PHYSICS Capacitance A pair of parallel plates will store electric energy if charged oppositely; this arrangement is called a capacitor. SEMESTER /2012

ENGINEERING PHYSICS Capacitance The charge is related to the potential difference; the ratio is called the capacitance. SEMESTER /2012 SI unit of capacitance: farad, F. For a parallel-plate capacitor, or The quantity inside the parentheses is called the permittivity of free space, ε 0.

ENGINEERING PHYSICS Capacitance The energy stored in a capacitor is the energy required to charge it: SEMESTER /2012

ENGINEERING PHYSICS Example A parallel plate capacitor with a plate of 0.5m x 0.5m and a plate separation of 6.00 mm is connected with 12 V source. Find: I) Charge on the capacitor ii) Energy stored in the capacitor Iii) Potential difference across the capacitor is reduce to half, explain what will happen to charge on the capacitor and its stored energy SEMESTER /2012

ENGINEERING PHYSICS Solution: I) ii) Iii) SEMESTER /2012 Since Q = CV, it half. Since UC = ½ CV 2, it doubles.

ENGINEERING PHYSICS Dielectrics A dielectric, or electrical insulator, is a substance that is highly resistant to the flow of an electric current. Although a vacuum is also an excellent dielectric, the following discussion applies primarily to physical substances. The use of a dielectric in a capacitor presents several advantages. The simplest of these is that the conducting plates can be placed very close to one another without risk of contact. Also, if subjected to a very high electric field, any substance will ionize and become a conductor. SEMESTER /2012

ENGINEERING PHYSICS Dielectrics “Dielectric” is another word for insulator. A dielectric inside a capacitor increases the capacitor’s energy storage by an amount characterized by the dielectric constant, . SEMESTER /2012

ENGINEERING PHYSICS Dielectrics A dielectric in an electric field becomes polarized; this allows it to sustain a larger electric field for the same potential difference. SEMESTER /2012 The net effect: E and V <<, Stored charge remains the same - Capacitance increase.

ENGINEERING PHYSICS Dielectrics The dielectric creates a ‘reverse’ electric field – that partially cancels the field between the plates. The  of the material is define as ratio of voltage with the material in place (V) to the vacuum voltage (V 0 ), and because V proportional to E, thus SEMESTER /2012 Only when the capacitor charge is constant  is dimensionless and > The capacitance of a capacitor containing a dielectric is increased. The definition for capacitance is or

ENGINEERING PHYSICS Dielectrics Inserting a dielectric into a capacitor while either the voltage or the charge is held constant has the same effect – the ratio of charge to voltage increases. SEMESTER /2012 Voltage drops Stored energy decrease Charge on a plates increase More energy stored in capacitor