Notes Electric Charge and Electric Field free essay sample

Electric charge is a fundamental property like mass, length etc associated with elementary particles for example electron, proton and many more. Electric charge is the property responsible for electric forces which acts between nucleus and electron to bind the atom together. Charges are of two kinds (i) negative charge (ii) positive charge Electrons are negatively charged particles and protons, of which nucleus is made of, are positively charged particles. Actually nucleus is made of protons and neutrons but neutrons are uncharged particles. electric force between two electrons is same as electric force between two protons kept at same distance apart i. e. , both set repel each other but electric force between an electron and proton placed at same distance apart is not repulsive but attractive in nature. Conclusion (a) Like charges repel each other (b) Unlike charges attract each other Assignment of negative charge on electron and positive charge on proton is purely conventional , it does not mean that charge on electron is less than that on proton. Importance of electric forces is that it encompasses almost each and every field associated with our life; being it matter made up of atoms or molecules in which electric charges are exactly balanced or adhesive forces of glue associated with surface tension, all are electric in nature. Unit Charge on a system can be measured by comparing it with the charge on a standard body. SI unit of charge is Coulomb written as C. 1 Coulomb is the charge flowing through the wire in 1 second if the electric current in it is 1A. Charge on electron is -1. 602 ? 10 -19 C and charge on proton is positive of this value. . Basic properties of electric charge (i) Additivity of charges Charges adds up like real numbers i. e. , they are Scalars more clearly if any system has n number of charges q1, q2, q3, qn then total charge of the system is q = q1 + q2 + q3 + . qn Proper sign have to be used while adding the charges for example if q1 = +1C q2 = -2C q3 = +4C then total charge of the system is q = q1 + q 2 + q3 q = (+1) + (-2) + (+4) C q = (+3) C (ii) Charge is conserved Charge of an isolated system is conserved. Chage can not be created or destroyed but charged particles can be created or estroyed. (iii) Quantization of charge All free charges are integral multiples of a unit of charge e, where e = -1. 602 ? 10 -19 C i. e. , charge on an electron or proton. Thus charge q on a body is always denoted by q = ne where n = any integer positive or negative 3. Frictional Electricity If we pass a comb through hairs, comb becomes electrically charged and can attract small pieces of paper. Many such solid materials are known which on rubbing attract light objects like light feather, bits of papers, straw etc. Explaination of appearance of electric charge on rubbing is simple. Material bodies consists of large number of electrons and protons in equal number and hence is in neutral in their normal state. But when the body is rubbed for example when a glass rod is rubbed with silk cloth, electrons are transferred from glass rod to silk cloth. The glass rod becomes positively charged and the silk cloth becomes negatively charged as it recieves extra electrons from the glass rod. In this case rod after rubbing, comb after passing through dry hairs becomes electrified and these are the example of frictional electricity. 4. Coulumbs law Coulombs law is the law of forces between electric charges. Statement It states that two stationary point charges q1 and q2 repel or attract each other with a force F which is directly proportional to the product of charges and inversly proportional to the square of distance between them. This dependence can be expressed by writing F? q1q2 r2 (1) These forces are attractive for unlike charges and repulsive for like charges . We now try to express Coulombs law in vector form for more clearity of magnitude and direction of forces. Consider two point charges q1 and q2 at points with position vector r1 and r2 with respect to the origin vector r21= r2 r1 is the difference between r2 and r1 and the distance of separation r is the magnitude of vector r21. pointwise it can be written as r1 = position vector of charge q1 with respect to origin r2 = position vector of charge q2 with respect to origin r21 = vector from 1 to 2 (r2 r1) r12 = -r21 = vector from 2 to 1 (r1 r2) r = r12 = r21 = distance between 1 and 2. Coulombs law can then be expressed as F21 = force on q2 due to q1 F21= kq1q2r21 3 (2a) and, F12 = force on q1 due to q2 F12= -F21 kq1q2r12 r3 (2b) Special Case for simplicity we can choose q1 being placed at origin r1 = 0 and if we write r2 = r the position vector of q2 then F21 = force on q2 due to q1 F21= kq1q2r r3 (3a) F12 = force on q1 due to q2 F12= kq1q2r r3 (3b) unit vector r? 21 and r? 12 can be defined as r? 21 = r21/r directed from q1 to q2 r? 12 = r12/r directed from q2 to q1 (4) -r21/r force c an now be written in terms of unit vector given as follows F21= kq1q2r? 21 r2 (5a) F12= kq1q2r? 12 r2 (5b) from this we can immidiately find factors giving magnitude and the directions in equation (2) we find a positive constant K and experimentally found value of k is K = 8. 98755 ? 10 9 Nm2/C2 K ? 9 ? 10 9 Nm2/C2 sometimes K is written as 1/4? ?0 where ? 0 is the permittivity of the vaccum whose value is K = 1/4 0 (? 0 = 9 ? 10 -12 C2/Nm2) 5. Principle Of Superposition Coulombs law gives the electric force acting between two electric charges. Principle of superposition gives the method to find force on a charge when system consists of large number of charges. According to this principle when a number of charges are interacting the total force on a given charge is vector sum of forces exerted on it by all other charges. This principle makes use of the fact that the forces with which two charges attract or repel one another are not affected by the presence of other charges. If a system of charges has n number of charges say q1, q2, .. qn, then total force on charge q1 according to principle of superposition is F = F12 + F13 + . F1n Where F12 is force on q1 due to q2 and F13 is force on q1 due to q3 and so on. F12, F13, F1n can be calculated from Coulombs law i. e. F12= kq1q2r? 12 4 0(r12)2 to, F1n= kq1q2r? 1n 4 0(r1n)2 The total force F1 on the charge q1 due to all other charges is the vector sum of the forces F12, F13, F1n. F1 = F12 + F13 + . The vector sum is obtained by parellogram law of addition of vector. Similarly force on any other charge due to remaining charges say on q2, q3 etc. can be found by adopting this method. 6. Electric Field Electrical interaction between charged particles can be reformulated using the concept of electric field. To understand the concept consider the mutual repulsion of two positive charged bodies as shown in fig (a) Now if remove the body B and label its position as point P as shown in fig (b), the charged body A is said to produce an electric field at that point (and at all other points in its vicinity) When a body B is placed at point P and experiences force F, we explain it by a point of view that force is exerted on B by the field not by body A itself. The body A sets up an electric field and the force on body B is exerted by the field due to A. An electric field is said to exists at a point if a force of electric origin is exerted on a stationary charged (test charge) placed at that point. If F is the force acting on test charge q placed at a point in an electric field then electric field at that point is E = F/q or F = qE Electric field is a vector quantity and since F = qE the direction of E is the direction of F. Unit of electric field is (N. C-1) Q. Find the dimensions of electric field Ans. [MLT-3A-1] 7. Calculation of Electric Field In previous section we studied a method of measuring electric field in which we place a small test charge at the point, measure a force on it and take the ratio of force to the test charge. Electric field at any point can be calculated using Coulombs law if both magnitude and positions of all charges contributing to the field are known. To find the magnitude of electric field at a point P, at a distance r from the point charge q, we imagine a test charge qto be placed at P. Now we find force on charge q due to q through Coulombs law. F= qq 4 0r2 electric field at P is E= q 4 0r2 The direction of the field is away from the charge q if it is positive Electric field for either a positive or negative charge in terms of unit vector r directed along line from charge q to point P is E= qr? 4 0r2 r = distance from charge q to point P. When q is negative , direction of E is towards q, opposite to r. Electric Field Due To Multiple Charges Consider the number of point charges q1, q2,.. which are at distance r1P, r2P,. from point P as shown in fig The resultant electric field is the vector sum of individual electric fields as E = E1P + E2P + This is also a direct result of principle of superposition discussed earlier in case of electric force on a single charge due to system of multiple charges. E is a vector quantity that varies from one point in space to another point and is determined from the position of square charges.