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ELECTRICITY ELECTRICITY

ELECTRICITY Dr. M D Mohammad h d Basha B h [email protected] fb2009@ il LECTURE C (1) Coulomb’ss Law Coulomb The Elementary Charge • It is the smallest charge which is the charge of g ) the Electron: e=1.6x10‐19C ((unit of charge) • The charged bodies can only have integral multiples of charge: e , thus: • The charge is quantized: q=Ze where Z=±1,±2,±3,….. • The charge is conserved (the algebraic net charge of any isolated system is constant) Conductors & Insulators • Consider how charge is carried on macroscopic objects. • W We will ill make k th the simplifying i lif i assumption ti th thatt th there are only two kinds of objects in the world: – Insulators: l In these h materials, l once they h are charged, h d the h charges ARE NOT FREE TO MOVE. Plastics, glass, and other “bad bad conductors of electricity electricity” are good examples of insulators. – Conductors: In these materials, the charges ARE FREE TO MOVE. Metals are good examples of conductors. Law of Electrical Force Charles Augustin Coulomb Charles‐Augustin 1785 " The repulsive force between two small spheres charged with the same sort of electricity is in the inverse ratio of the squares of the distances between the centers of the spheres" h " q1 q2 r q1q2 F 2 r Coulomb's Law • Coulomb determined – Force is attractive if charges are opposite sign – Force proportional to the product of the charges q1 and q2 along the lines joining them – Force inversely proportional to square of the distance  q1q2 F k 2 r Coulomb's Law • Units of constant (k) can be determined from Coulomb'ss Law Coulomb • Colomb (and others since) have determined this constant which ((in a vacuum)) in SI units is k = 9x109 Nm2C‐2 • k is normally expressed as k = 1/40 where 0 is the permittivity of free space 12 C2/N/m2 0=8.85x10 =8 85x10‐12 What We Call Coulomb'ss Law Coulomb q1  r12 MKS Units Units: • r in meters • q in Coulombs •  F • r̂ˆ12 is in Newtons a unit vector pointing from 1 to 2 q2  F12  The force from 1 acting on 2 q1q2 rˆ12 2 4 0 r12 1  q1q2 F k 2 r • This force has same spatial dependence as the gravitational force, BUT there is NO mention of mass here!! • The strength of the force between two objects is determined by the charge of the two objects, and the separation between them. Coulomb Law Qualitative q1 q2 r • What happens if q1 increases? F (magnitude) increases •What happens if q1 changes sign ( +  Th direction The di ti off F is i reversed d • What happens if r increases? F (magnitude) decreases - )? Vector form of Coulomb’s Coulomb s Law F12 r12 + ‐ Q2 F12 r̂12 + F21 F21 Q1 + Quiz 1 Object A has a charge of +2 C and Object B g of +6  C. Which statement is has a charge true? F ? BA A +2 C FAB? B +6 C • • • • A: FAB=‐3F 3FBA B: FAB==‐FFBA C: 3FAB=‐FBA D: FAB=12FBA Quiz 2 +Q • Two balls, one with charge Q1 = +Q and the other with charge Q2 = +2Q, are held fixed at a separation d = 3R as shown. Q1 • Another ball with (non-zero) charge Q3 is introduced in between Q1 and Q2 at a distance = R from Q1. +Q – Which of the following statements is true? Q1 +2Q Q2 3R +2Q Q3 R The force on Q3 can be zero if Q3 is positive. The force on Q3 can be zero if Q3 is negative. Q2 2R ((a)) (b) Th force f on Q3 can never be b zero, no matter tt what h t the th (c) The (non-zero) charge Q3 is. The magnitude of the force on Q3 due to Q2 is proportional to (2Q Q3 /(2R)2) The magnitude of the force on Q3 due to Q1 is proportional to (Q Q3 /R2) These forces can never cancel, because the force Q2 exerts on Q3 will always be 1/2 of the force Q1 exerts on Q3!! Force from many charges Superposition What happens when you consider d more than h two charges? h ? • If q1 were the only other charge charge, we would know the force on q due to q1 . • If q2 were the only y other charge, g we would know the force on q due to q2 . •  F1 q What is the force on q when both q1 and q2 are present? t? – The answer: just as in mechanics, we have h the th Law L off Superposition: S iti • The TOTAL FORCE on the object is just the VECTOR SUM of the individual forces.   F = F1 +  F2 +q1  F ® F2 +q2 Force from many charges F41 ‐ F21 Q1 Q2 + ‐ F31 Principle of superposition p p + Q3 Force on charge is vector sum of forces from all charges Q4 F1  F21  F31  F41 Example qo, q1, and q2 are all point charges where qo = -1mC, q1 = 3mC, and q2 = 4mC. Their locations are shown in the diagram.  What is the force acting on qo ( F0) ?    We have F0  F10  F20   Find F10 and F20 q0 q1 F10  k 2 r10 qq F20  k 0 2 2 r20   F10   F10 ˆj F20  F20 x iˆ  F20 y ˆj y (cm) 4 3 qo 2 1 θ q1 1 2 3 4 q2 5 x (cm) What are F0x and F0y ?  F20 into its x and y Decompose p components  F 20  F 20 cos  cos   x2  x0 r20 iˆ  F 20 sin  ssin   y0  y 2 r20 ˆj Example continued y (cm) qo, q1, and q2 are all point charges where h qo = -1mC, 1 C q1 = 3mC, 3 C and d q2 = 4mC. Their locations are shown in the diagram diagram. 4 3  F20 qo  2 F10 1  F0 q1 q2 1 2 3   Now add the components of F10 and F20 to find F0 x and F0 y F0 x  F10 x  F20 x F0 x  F20 cos  F0 y  F10 y  F20 y F0 y   F10  F20 s i n  4 5 x (cm) Example continued y (cm) qo, q1, and q2 are all point charges where qo = -1mC, 1mC, q1 = 3mC, and q2 = 4mC. Their locations are shown in the diagram. 4 3  F20 qo  2 F10 1  F0 q1 q2 1 2 3 4 5 x (cm) Let’s et s put in tthe e numbers u be s . . . cos   0.8 sin   0.6 r10  3cm r20  5cm F10  30 N F20  14.4 N F0 x  11.52 N F0 y  38.64 N FO  11.52iˆ  38.64 ˆj  The magnitude of F0 is F0  F02x  F02y  40.32 N Coulomb’s Law vs Newton’s Law of Gravity m1m2 Q1Q2 rr̂ F12  rˆ F12  G 2 12 2 12 | r12 | 4 0 | r12 | 1 • • • • Attractive or repulsive /2 1/r very strong only relevant relatively local scales • • • • e2  Gm 2 4 0 Always attractive 1/r2 very weak p on veryy important large scales, planets, the Universe Summary y • Charges come in two varieties – negative and positive – in a conductor, negative charge means extra mobile electrons, and positive charge means a deficit of mobile electrons  1 qq • Coulomb Force F12  – bi-linear in charges g 4o r 1 2 2 12 12 rˆ – inversely proportional to square of separation – central force • Law of Superposition F1  F21  F31  F41  ......