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Transcript
0 Physics 213 General Physics Lecture 2 Last Meeting: Electric Charge, Conductors/Insulators Today: Static Charges, Conductors, Coulomb’s Law, Electric Forces, Electric Field 2 Demo Glass, Silk, Amber, Fur conduction/induction 3 Charging by Conduction A charged object (the rod) is placed in contact with another object (the sphere) Some electrons on the rod can move to the sphere When the rod is removed, the sphere is left with a charge The object being charged is always left with a charge having the same sign as the object doing the charging 4 Charging by Induction • When an object is connected to a conducting wire or pipe buried in the earth, it is said to be grounded • A neutral sphere has equal number of electrons and protons Polarization In most neutral atoms or molecules, the center of positive charge coincides with the center of negative charge In the presence of a charged object, these centers may separate slightly This results in more positive charge on one side of the molecule than on the other side surface of the insulator This realignment of charge on the surface of an insulator is known as polarization A charged comb attracts bits of paper due to polarization of the paper 6 Demo Comb and Paper Pivoting Plank 7 Demo Van de Graaff Generator 8 Van de Graaff Generator Charge is transferred to the dome by means of a rotating belt 10 11 Vector Nature of Electric Forces Two point charges are separated by a distance r The like charges produce a repulsive force between them The force on q1 is equal in magnitude and opposite in direction to the force on q2 12 Vector Nature of Forces, cont. Two point charges are separated by a distance r The unlike charges produce a attractive force between them The force on q1 is equal in magnitude and opposite in direction to the force on q2 13 Vector Nature of Electric Forces Magnitude of the force |q1||q2| Fk 2 r In the direction of r12 qq F12 k 122 r r12 r21 r12 The precise Coulomb’s law q q 1 2 ˆ ˆ F k r r i s a u n i t v e c t o r ) 1 2 2( 1 2 21 r 14 Unit Vectors A unit vector is a dimensionless vector with a magnitude of exactly 1. Unit vectors are used to specify a direction Reference: Serway and Vuille, 8th ed. Chapter 3. 15 Unit Vectors, cont. The symbols iˆ, ˆj, and kˆ represent unit vectors They form a set of mutually perpendicular vectors Right-hand convention 16 Unit Vectors in Vector Notation Ax is the same as Ax î and Ay is the same as Ay ĵ etc. The complete vector can be expressed as ˆ ˆ ˆ A A i A j A k x y z 17 Adding Vectors Using Unit Vectors Using R = A + B Then R Aˆ iAˆ j Bˆ iBˆ j x y x y ˆ ˆ R A B i A B x x y y j R R R x y and so Rx = Ax + Bx and Ry = Ay + By R R R R t a n R x 2 x 2 y 1y 18 Vector Nature of Forces, cont. Two point charges are separated by a distance r The unlike charges produce an attractive force between them The force on q1 is equal in magnitude and opposite in direction to the force on q2 q q q q 1 2 1 2 ˆ ˆ F k r F k r (act rea p 12 12 21 21 2 2 r r 19 Question: Four point charges, each of the same magnitude, with varying signs are arranged at the corners of a square as shown. Which of the arrows labeled A, B, C, and D gives the correct direction of the net force that acts on the charge at the upper right corner? a. A b. B c. C d. D e. The net force on that charge is zero Answer: b 20 21 Answer: 1 4 Consider first the force from 1 on 4. 3 2 We will now do the forces from the other charges on 4. We can add up all three force vectors to determine the net force on 4. 22 1 Answer: Q 2 F1 x k a2 Q 2 F2 y k a2 QQ F3 k 2a 2 in th e d ir e c tio n D 3 4 2 Q2 1 F3 x F3 c o s 4 5 k 2a2 2 Q2 1 F 3 y F 3 s in 4 5 k 2a2 2 F x F1 x F 3 x 0 F y F2 y F3 y 0 T h e a n s w e r is B . Superposition Principle 23 m1m2 F G 2 r 24 Q 25 q | E ( r ) | k 2 r Faraday introduced electric field and electric field lines which are said to exist in the region of space around a charged object. When another charged object enters this electric field, the field exerts a force on the second charged object 26 27 Coulombs force and electric fields. q1q2 F12 k 2 r̂12 r q1q2 F12 k 2 r̂12 r q1 E1 k 2 r̂12 r q2 qtest Superposition Principle q4 q3 q1 Direction of Electric Field The electric field produced by a negative charge is directed toward the charge A positive test charge would be attracted to the negative source charge 29 Direction of Electric Field, cont The electric field produced by a positive charge is directed away from the charge A positive test charge would be repelled from the positive source charge 30 Question: An electron traveling horizontally enters a region where a uniform electric field is directed upward.What is the direction of the force exerted on the electron once it has entered the field? (a) to the left (b) to the right (c) upward (d) Downward (e) out of the page, toward the reader Answer: d 31 Rules for Drawing Electric Field Lines 1. The lines for a group of charges must begin on positive charges and end on negative charges In the case of an excess of charge, some lines will begin or end infinitely far away 2. The number of lines drawn leaving a positive charge or ending on a negative charge is proportional to the magnitude of the charge 3. No two field lines can cross each other Electric Field Line Patterns Point charge The lines radiate equally in all directions For a positive source charge, the lines will radiate outward Electric Field Line Patterns For a negative source charge, the lines will point inward Electric Field Line Patterns An electric dipole consists of two equal and opposite charges The high density of lines between the charges indicates the strong electric field in this region Electric Field Line Patterns Two equal but like point charges At a great distance from the charges, the field would be approximately that of a single charge of 2q The bulging out of the field lines between the charges indicates the repulsion between the charges The low density of field lines between the charges indicates a weak field in this region Electric Field Patterns Unequal and unlike charges Note that two lines leave the +2q charge for each line that terminates on -q