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## Chapter 21

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**Chapter 21**Electric Charge and Electric Field**Introduction**• Water makes life possible as a solvent for biological molecules. What electrical properties allow it to do this? • We now begin our study of electromagnetism, one of the four fundamental forces in Nature. • We start with electric charge and electric fields.**Goals for Chapter 21**• Study electriccharge & charge conservation • Learn how objects become charged • Calculate electric force between objects using Coulomb’s law F = k|q1q2|/r2 = (1/4π0)|q1q2|/r2 • Learn distinction between electric force and electric field**Goals for Chapter 21**• Calculatethe electric field due to many charges • Visualizeand interpret electric fields • Calculate the properties of electric dipoles**Goals for Chapter 21**• Be able to solve this kind of problem: (page 715) Charge Q is distributed uniformly around a semicircle of radius a. What is the magnitude and direction of the resulting E field at point P, at the center of curvature of the semicircle? y Charge Q a x P**Physics from 4A you will need to know!**• Forces as vectors • Establish coordinate frame • Break into components Fx, Fy, Fz • Add like components! • Resolve net vector • Answers must have three things! • Magnitude • Direction • UNITS**Physics from 4A you will need to know!**• Chapter 4: Forces • “Links in a Chain” page 127 • Exercises/Problems 4.2, 37, 54, 62* (calculus) • Chapter 5: Applications • Section 5.2 (Dynamics) ex 5.10, 5.11, 5.12 • Section 5.4 (Circular) ex 5.20, 5.21 • “In a Rotating Cone” page 162**Math from 4A you will need to know!**• Integration of continuous variables**Electric charge**• Two positiveor two negativecharges repel each other. A positive charge and a negative charge attract each other. • Check out: http://www.youtube.com/watch?v=45AAIl9_lsc**Electric charge**• Two positiveor two negativecharges repel each other.A positive charge and a negative charge attract each other.**Electric charge**• Two positiveor two negativecharges repel each other.A positive charge and a negative charge attract each other. • Check out Balloons in PhET simulations**Electric charge and the structure of matter**• The particles of the atom are the negative electron, the positive proton, and the uncharged neutron.**You should know this already: Atoms and ions**• A neutral atom has the same number of protons as electrons. • A positive ion is an atom with one or more electrons removed. A negative ion has gained one or more electrons.**Conservation of charge**• Proton & electron have same magnitude charge.**Conservation of charge**• Proton & electron have same magnitude charge. • All observable charge is quantizedin this unit. “½ e”**Conservation of charge**• Proton & electron have same magnitude charge. • Universal principleofchargeconservationstates algebraic sum of all electric charges in any closedsystem is constant. +3e – 5e +12e – 43e = -33 e**Conductors and insulators**• A conductor permits the easy movement of charge through it. An insulator does not. • Most metals are good conductors, while most nonmetals are insulators.**Conductors and insulators**• A conductorpermits the easy movement of charge through it. • An insulatordoes not.**Conductors and insulators**• Semiconductorsare intermediate in their properties between good conductors and good insulators.**Charging by induction**• Start with UNCHARGED conducting ball…**Charging by induction**• Bring a negatively charged rod near – but not touching.**Charging by induction**• Bring a negatively charged rod near – but not touching. • The negative rod is able to charge the metal ball without losing any of its own charge.**Charging by induction**• Now connect the conductor to the ground (or neutral “sink”) • What happens?**Charging by induction**• Now connect the conductor to the ground (or neutral “sink”) • Conductor allows electrons to flow from ball to ground…**Charging by induction**• Connect the conductor to the ground (or neutral “sink”)**Charging by induction**• The negative rod is able to charge the metal ball without losing any of its own charge.**Electric forces on uncharged objects**• The charge within an insulator can shift slightly. As a result, an electric force *can* be exerted upon a neutral object.**Electrostatic painting**• Induced positive charge on the metal object attracts the negatively charged paint droplets. Check out http://www.youtube.com/watch?feature=endscreen&v=zTwkJBtCcBA&NR=1**Q21.1**When you rub a plastic rod with fur, the plastic rod becomes negatively charged and the fur becomes positively charged. As a consequence of rubbing the rod with the fur, A. the rod and fur both gain mass. B. the rod and fur both lose mass. C. the rod gains mass and the fur loses mass. D. the rod loses mass and the fur gains mass. E. none of the above**A21.1**When you rub a plastic rod with fur, the plastic rod becomes negatively charged and the fur becomes positively charged. As a consequence of rubbing the rod with the fur, A. the rod and fur both gain mass. B. the rod and fur both lose mass. C. the rod gains mass and the fur loses mass. D. the rod loses mass and the fur gains mass. E. none of the above**Q21.2**A positively charged piece of plastic exerts an attractive force on an electrically neutral piece of paper. This is because A. electrons are less massive than atomic nuclei. B. the electric force between charged particles decreases with increasing distance. C. an atomic nucleus occupies only a small part of the volume of an atom. D. a typical atom has many electrons but only one nucleus.**A21.2**A positively charged piece of plastic exerts an attractive force on an electrically neutral piece of paper. This is because A. electrons are less massive than atomic nuclei. B. the electric force between charged particles decreases with increasing distance. C. an atomic nucleus occupies only a small part of the volume of an atom. D. a typical atom has many electrons but only one nucleus.**Coulomb’s law – Electric FORCE**• The magnitude of electric force between two point charges is directly proportional to the product of their charges andinversely proportionalto the square of the distance between them.**Coulomb’s law**• Mathematically: F = k|q1q2|/r2= (1/4π0)|q1q2|/r2 • A VECTOR • Magnitude • Direction • Units**Coulomb’s law**• Mathematically: |F| = k|q1q2|/r2 • “k” = 9 x 109 Newton meter2/Coulomb2 • “k” = 9 x 109Nm2/C2**Coulomb’s law**• Mathematically: |F| = k|q1q2|/r2= (1/4π0)|q1q2|/r2 • e0= 8.85 x 10 – 12 C2/Nm2 • e0 =“Electric Permittivity of Free Space”**Measuring the electric force between point charges**Example 21.1 compares the electric and gravitational forces. An alpha particle has mass m = 6.64 x 10-27 kg and charge q = +2e = 3.2 x 10-19 C. Compare the magnitude of the electric repulsion between two alpha particles and their gravitational attraction**Measuring the electric force between point charges**DRAW the VECTORS!! An alpha particle has mass m = 6.64 x 10-27 kg and charge q = +2e = 3.2 x 10-19 C. Compare the magnitude of the electric repulsion between two alpha particles and their gravitational attraction**Measuring the electric force between point charges**An alpha particle has mass m = 6.64 x 10-27 kg and charge q = +2e = 3.2 x 10-19 C. Fe/Fg = ? Remember Fg = Gm1m2/r2 & G= 6.67 x 10-11 Nm2/kg2**Measuring the electric force between point charges**An alpha particle has mass m = 6.64 x 10-27 kg and charge q = +2e = 3.2 x 10-19 C. Fe/Fg = 3.1 x 1035!!!!**Force between charges along a line**• Example 21.2 for two charges: Two point charges, q1 = +25nC, and q2 = -75 nC, separated by r = 3.0 cm. What is the Force of q1 on q2? What is the Force of q2 on q1?**Force between charges along a line**• Example 21.2 for two charges: Two point charges, q1 = +25nC, and q2 = -75 nC, separated by r = 3.0 cm. What is the Force of q1 on q2? Step 1: Force is a vector – create a coordinate system FIRST! x**Force between charges along a line**• Example 21.2 for two charges: Two point charges, q1 = +25nC, and q2 = -75 nC, separated by r = 3.0 cm. What is the Force of q1 on q2? What is the force of q2 on q1?**Force between charges along a line**• Example 21.2 for two charges: Two point charges, q1 = +25nC, and q2 = -75 nC, separated by r = 3.0 cm. What is the Force of q1 on q2? What is the force of q2 on q1?**Force between charges along a line**• Example 21.2 for two charges: Two point charges, q1 = +25nC, and q2 = -75 nC, separated by r = 3.0 cm. What is the Force of q1 on q2? F of q1 on q2 = F12 = 0.019N <-x> F12 x**Force between charges along a line**• Example 21.3 for three charges: Two point charges, q1 = +1.0nC at x = +2.0 cm, and q2 = -3.0 nC at x = +4.0 cm. What is the Force of q1 and q2 on q3 = + 5.0 nCat x = 0?**Force between charges along a line**• Example 21.3 for three charges: Two point charges, q1 = +1.0nC at x = +2.0 cm, and q2 = -3.0 nC at x = +4.0 cm. What is the Force of q1 and q2 on q3 = + 5.0 nCat x = 0?**Vector addition of electric forces**• Example 21.4 shows that we must use vector addition when adding electric forces. Two equal positive charges, q1 = q2 = +2.0mC are located at x=0, y = 0.30 m and x=0, y = -.30 m respectively. What is the Force of q1 and q2 on Q = + 5.0 mC at x = 0.40 m, y = 0?**Vector addition of electric forces**• Example 21.4 shows that we must use vector addition when adding electric forces.