Title Med-RM_Phy_SP-3_Ch-16_Electric Charges and Fields.pdf ✅

Chapter Contents Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Introduction Electric Charges Methods of Charging Coulomb’s Law Electric Field Electric Field Lines Motion of a Charged Particle in a Uniform Electric Field Electric Dipole Dipole in a Uniform External Field Continuous Charge Distribution Electric Flux Gauss’s Law Applications of Gauss’s Law Introduction In this chapter, we essentially deal with static electricity. Static means anything that does not move or change with time. The study of static charges is called electrostatics. ELECTRIC CHARGES It is the intrinsic property of certain particles, like mass, by which they can interact with other charged particles. Properties of Charge (i) There exist two different kind of charges, one that on electron and another that on proton. By convention, charge on an electron is taken as negative and charge on a proton is taken as positive. (ii) Like point charges repel each other and unlike point charges attract each other. (iii) Electric charge is conserved i.e., total charge of the universe remains constant. (iv) Electric charge is quantized. In all macroscopic considerations, charge always exists as an integral multiple of electronic charge. q = ± ne where e = 1.6 × 10–19 coulomb. When q = 1 coulomb, n = 6.25 × 1018 (subatomic particles like quarks have charge 3 e down quark and 2 3 e up quark. But they do not exist freely) (v) Charge unlike mass is invariant. It does not vary with speed of the particle. (vi) Charge cannot exist without mass, while mass can exist without charge. (vii) Charge is a scalar quantity. (viii) Charge is always additive in nature. Units of Charge It is a derived physical quantity having dimensional formula [AT] and its unit (ampere × second) is called coulomb. 1 coulomb = 3 × 109 e.s.u. of charge = 1 10       e.m.u. of charge. Chapter 16 Electric Charges and Fields
80 Electric Charges and Fields NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Example 1 : What is the total charge of a system containing five charges +1, +2, –3, +4 and –5 in some arbitrary unit? Solution : Total charge is +1 + 2 – 3 + 4 – 5 = –1 in the same unit. Example 2 : How many electrons are there in one coulomb of electricity? Solution : Remember electricity means charge. Use the formula Q = ne  18 –19 1 coulomb 6.25 10 electrons 1.6 10 coulomb Q n e      . You may observe that if an electron does not have integral value of charge, then all charges must be in fraction and how do we have one coulomb which is an integer! Our argument is that there are too many electrons in one coulomb. So even if one electron is removed it will not affect the integral value of charge. (It is something like if you take out one small bucket of sea water, it will not affect the sea level). At such a large value of charge equal to one coulomb, it is a good approximation to regard charge as continuous, much the same way as we regard matter to be continuous at macroscopic level even though it is composed of atoms and molecules. METHODS OF CHARGING Charging by Friction When two bodies are rubbed with each other, there is a transfer of electrons from one body to other. A B (Both are Neutral) Rubbed A B A B e e e Mass decreases Mass increases + – Charging By Induction When a charged body is brought near an uncharged body, there appears a charge on the surface of uncharged body due to attractive / repulsive forces between charges as shown. The induced charge can be lesser or equal to the inducing charge. It’s value is given by, qin = –q 1 1 k        where k is the dielectric constant of the material of uncharged body. A B Neutral A B Net charge = 0 + + + + + + + + – – – – + + + + – – – – + + + + – + – – – –
NEET Electric Charges and Fields 81 Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 COULOMB’S LAW Coulomb measured the force between two point charges and found that is varied inversely as the square of the distance between the charges and was directly proportional to the product of magnitude of the two charges and acted along the line joining the two charges. Q1 Q2 r If two point charges Q1 and Q2 are at rest and separated by a distance r in vacuum, the magnitude of force between them is given by 1 2 2 k QQ F r  . The constant k is usually put as 0 1 4 k   Where 0 is called the permittivity of free space and has the value 0 = 8.854 × 10–12 C2 N–1 m–2. For all practical purposes we will take 9 22 0 1 9 10 N m / C 4    . In medium net force becomes 1 2 2 1 4   Q Q F r where is permittivity of medium between charges 0  r (r is relative permittivity or dielectric constant of medium). Example 3 : A proton and an electron are placed 1.6 cm apart in free space. Find the magnitude and nature of electrostatic force between them. Solution : Using Coulomb’s law      9 –19 –19 1 2 –25 2 2 –2 0 9 10 1.6 10 –1.6 10 –9 10 N 4 1.6 10 Q Q F r          Negative sign indicates that the force is attractive in nature. Example 4 : Nucleus 92U238 emits -particle (2He4). At any instant -particle is at distance of 9 × 10–15 m from the centre of nucleus of uranium. What is the force on -particle at this instant ? 238 4 234 92U He Th   2 90 Solution : 1 2 2 0 1 4   q q F R 92U238 has charge 92e. When -particle is emitted, charge on residual nucleus is 92e – 2e = 90e  q1 = 90e, q2 = 2e, and R = 9 × 10–15 m  F = 9 –15 2 (90 )(2 ) 9 10 (9 10 )    e e = 9 –19 2 –15 2 9 10 90 (1.6 10 ) 2 (9 10 )      = 512 N
82 Electric Charges and Fields NEET Aakash Educational Services Limited - Regd. Office : Aakash Tower, 8, Pusa Road, New Delhi-110005 Ph. 011-47623456 Coulomb’s Law in Vector Form Let the position vector of charges q1 and q2 be 1 r and 2r respectively. q2 q1 r1 r2 F12 F21 r r r 21 2 1 = – z y x We denote force on q1 due to q2 by F12 and force on q2 due to q1 by F21 . Force on charge q2 due to q1 , 1 2 -21 21 2 0 21 1 · 4 q q F r r   . The equation above is valid for any sign of q1 and q2 whether positive or negative. Force on charge q1 due to charge q2 1 2 -12 2 12 21 0 12 1 – 4 q q F rF r    Thus, Coulomb’s law agrees with the Newton’s third law. The principle of superposition : It states that net force on a given charge is equal to the vector sum of individual forces exerted by various charges, on the charge. q3 q1 qn q0 q2 Net force on charge q0 0 01 02 03 0 ........ FF F F F   n Example 5 : Two fixed charges +4q and +q are at a distance 3 m apart. At what point between the charges, a third charge +q must be placed to keep it in equilibrium? Solution : Remember if Q1 and Q2 are of same nature (means both positive or both negative) then the third charge should be put between (not necessarily at mid-point) Q1 and Q2 on the straight line joining Q1 and Q2. But if Q1 and Q2 are of opposite nature, then the third charge will be put outside and close to that charge which is lesser in magnitude. q Q q 2 Q q 1 = +4 = + x 3–x Here you can see Q1 and Q2 are of same nature so third charge q will be kept in between at a distance x from Q1 (as shown in figure). Hence, q will be at a distance (3 – x) from Q2. Since q is in equilibrium, so net force on it must be zero. You can see, the forces applied by Q1 and Q2 on q are in opposite direction, so just balance their magnitude. Force on q by 1 1 2 kQ q Q x  and that by 2 2 2 (3 – ) kQ q Q x  Now, 1 2 2 2 (3 – ) kQ q kQ q x x  or 1 2 2 2 (3 – ) Q Q x x  or 2 2 4 1 x (3 – ) x  Take the square root; 2 1 x (3 – x) 