Physics II (PH2223) Physics for Scientists and Engineers, with Modern Physics, 4th edition, Giancoli

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1 Physics II (PH2223) Physics for Scientists and Engineers, with Modern Physics, 4th edition, Giancoli

2 Topics Covered Electric Charge & Electric Field Electric Potential Capacitance, Dielectric, Electric Energy Storage Electric Currents & Resistance DC Circuits Magnetism Sources of Magnetic Field Electromagnetic Induction & Faraday s Law Inductance, Electromagnetic Oscillations, and AC Circuits

3 Electric Charge & Electric Field

4 Electric Charge " Electric charge is a property of matter. " Charge is either positive or negative; attractive forces between unlike charges and repulsive forces between like charges. " Charge is conserved (symmetry of nature). " Charge is quantized (there are no free charged particles with charge less than that of an electron). " Charge is a multiple of the electron or proton charge: e = "19 C

5 " Ordinary matter is made up of atoms which have positively charged nuclei (protons and neutrons) and negatively charged electrons surrounding them. " Conductors: Matter # Solid: one or more of the bound electrons can move freely in material. # Some solids or liquids: ions are able to move about and give rise to currents (electrolytes). # Gasses: neutral atoms or molecules become ionized (external). " Insulators or dielectrics: Electric charges do not freely move. " Semiconductors: some bound charges are able to move (by thermal vibration, light, electric field, ). " The Earth: Can be considered to be an infinite reservoir of (or for) electrons, i.e., it can accept or supply an unlimited number of electrons.

6 Electrostatics Electrostatics deals with the phenomena and properties of stationary or slow-moving charges, which involves the buildup of charge on the surface of objects. Induction: A negatively charged object repels electrons from the surface of a second object.

7 Coulomb's Law Two electric charges experience electrostatics force between them such that: # It is proportional to the square of the separation r between the 2 particles along the line that joins them # It is proportional to the product of the magnitude of the charges, q and Q, on the two particles. # It is attractive if the charges are of opposite sign and repulsive if the charges have the same sign. F = k qq r 2 k = 1 $ N #m 2 ' 9 "10 9 4" 0 % & C 2 ( ) ˆr " # " # $

8 Problem (1) Two balls, one with charge Q 1 = +Q and the other with charge Q 2 = +2Q, are held at a separation d. Is there any place between Q 1 and Q 2 where the force on any charge (+ or -) is zero?

9 Electric Field " Test charge does not exert force on other charges, hence does not disturb the charges in the vicinity. In practical situations, a test charge can be approximated by a charge of nearly negligible magnitude. " Electric field exists at any point in space where a test charge, if placed at that point would experience an electric force. The electric field is a vector quantity. The direction of the electric field at a point is the same as direction of the force experienced by a positive test charge placed at that point. F = q E 0 0 similar to F = m g g 0

10 Electric Field Lines An electric charge emits an electric field which always points towards a negative charge and points away from a positive charge: Note that only a few of the possible field lines are drawn and the field is continuous and exists between the lines.

11 Electric Field Lines " A system of charged particles: # The lines must begin on positive charges and must terminate on negative charges # The number of lines leaving a positive charge or approaching a negative charge is proportional to the magnitude of the charge. # No two field lines can cross each other. " Drawing electric field lines: # The electric field vector, E, is tangent to the electric field lines at each point. # The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the E-field in a given region.

12 Problem (2) Based on the Figure to the right, which of the following is correct? A. q1 = q2 B. q2 is positive and q1 negative; q1 > q2 C. q1 is positive and q2 negative; q1 > q2 D. q2 is positive and q1 negative; q2 > q1

13 Electric Field of a Point Charge " If a small test charge q 0 is placed at a distance r from charge q, it will experience a force (Coulomb force) F = 1 4" 0 qq 0 r 2 " If a point charge q 0 is placed at a position where the electric field is E, then the force on q 0 is F = q 0 E " Comparing these two expressions for F, we see that E = 1 4" 0 q r 2

14 Problem (3) An alpha particle (charge +2e) is sent at high speed toward a gold nucleus (charge +79e). What is the electrical force acting on the alpha particle when it is m from the gold nucleus? Is the Coulomb force a repulsion force or an attraction force?

15 Superposition Principal If more than two charged particles exist in a system, then the Coulomb force exerted on one particle is the summation of all of the Coulomb forces between that particle and the rest of the particles in the ensemble: F = 1 N N q i q # 0 ˆr i = # F i ˆx + F i ŷ 4" 0 i r i 2 i # + F i ẑ i N # i Similarly, the electric field E at a point due to several charges is the vector sum of the fields due to the individual charges. E = 1 q # i 2 4" 0 r ˆr i i i For a continuous charge distribution we can write: E = 1 dq # 4" 0 r 2 ˆr

16 Electric Field: System of Charges When summing E-fields from multiple charges, it is best to draw a vector diagram first at a point where the E-field is to be determined. Draw the E-field vector of each charge in the direction as dictated by E = 1 4" 0 q r 2 ˆr. Then vectorially add the individual E-fields together, letting the diagram determine the sign of the E-field. Then add using the absolute value of the charge: n 1 ( ) E = ± 1 4"# 0 q r 2. The + or - is selected based upon the direction of the E-field vector.

17 Problem (4) Positive charges are situated at three corners of a rectangle as shown in the figure below. Find the electric field at the fourth corner.

18 Charge Distribution The simplest kind of charge distribution is a point charge. If the dimensions of the charge distribution are much less than the distance away from a point of interest, it can be considered a point charge. If the dimensions must be considered, then the charge density can be useful. Volume density Area density Linear density = dq ( dv C ) m3 = dq ( da C ) m2 = dq dl In the special case for uniform charge density, we have: = q ( V C ) m3 = q ( A C ) m2 = q l ( C m) ( C m)

19 Problem (5) A rod of length 2a has a uniform positive charge per unit length, and a total charge Q. Calculate the electric field at a point P, a distance x along the perpendicular bisector of the rod.

20 Electric Dipole An electric dipole is an important case of a two-charge distribution, which consists of a pair of point charges with equal magnitude and opposite sign, +Q and Q, separated by a fixed distance d. Let's take the magnitude of r + and r to be equal to r, r + = rsin" ˆx r cos"ŷ r ˆr + = + r = sin" ˆx cos"ŷ E + = 1 Q + ˆr 4#$ 0 r 2 + = 1 Q + 4#$ 0 r 2 E = 1 Q ˆr 4#$ 0 r 2 = 1 Q 4#$ 0 r 2 E total = E + + E = 1 Q 4#$ 0 r 2 1 4#$ 0 Q r 2 ( sin" ˆx cos"ŷ) + (sin" ˆx cos"ŷ) ( sin" ˆx cos"ŷ) (sin" ˆx cos"ŷ) E total = 1 4"# 0 Q r 2 ( 2cos$ )ŷ

21 Torque & Force on an Electric Dipole An important property of an electric dipole is the torque exerted on it by a uniform electric field. The torque is given by #% = r " F $ &% F = q E ' = r " q E = ( d 2)qE sin" + ( d 2)qE sin" = dqe sin" The product of the charge q and the separation d is called electric dipole moment, denoted by p. Electric dipole moment, p, is a vector quantity and its direction is defined from q to +q. Potential energy of a dipole in an electric field is: = p " E U = p " E

22 Motion of Charged Particles in a Uniform Electric Field Similar to projectile motion (from physics I) and Newton s Second Law: a x = 0 and a y = (e)e m # t = 0 " x = y = $ % v 0 x = v 0 and v 0 y = 0 # x = v 0 t & t > 0 " $ y = 1 2 a yt 2 = y = 1 % & 2 y = 1 ee 2 2 mv x2 0 F = qe = ma a = qe m ee m t 2

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