PHY 184 Spring 2007 Lecture 3 Title The Coulomb Force 1 10 2006 184 Lecture 3 1 Announcements Don t forget to register your clicker Homework Set 1 is due Tuesday January 16 at 8 00 am We will soon post the complete SLC schedule Strosacker Learning Center Room 1248 B P S 1 10 2006 184 Lecture 3 2 Outline 1 Review 2 Electrostatic charging 3 Coulomb s Law 1 10 2006 184 Lecture 3 3 Review There are two types of charge negative and positive Most objects are electrically neutral they have equal numbers of negative and positive charges net charge is 0 An object becomes charged by adding or removing electrons An electron carries negative charge of magnitude e 1 602 10 19 C Law of Charges Like charges repel and opposite charges attract Law of charge conservation The total charge of an isolated system is strictly conserved Conductors are materials where some of the electrons can move freely Insulators are materials where none of the charges can move freely 1 10 2006 184 Lecture 3 4 Electrostatic Charging There are two ways to charge an object Conduction Induction Charging by conduction We can charge an object by connecting a source of charge directly to the object and then disconnecting the source of charge The object will remain charged Conservation of charge 1 10 2006 184 Lecture 3 5 Charging by Conduction Electroscope We brought charge onto the electrode by contact 1 10 2006 184 Lecture 3 6 Induction Induction The presence of the positively charged rod leads to a redistribution of charge a kind of polarization It pulls electrons up to the electrode 1 10 2006 184 Lecture 3 7 Charging by Induction We can also charge an object without physically connecting to it First we charge a rod positively Then we ground the object to be charged Connecting the object to the Earth provides an effectively infinite sink for charge We bring the charged rod close to the object but do not touch it We remove the ground connection and move the rod away The object will be charged by induction 1 10 2006 184 Lecture 3 8 Charging by induction Induction The presence of the positively charged rod leads to a redistribution of charge Grounding pushes positive charge to Earth or rather pulls electrons from Earth leaving the electroscope negative ground 1 10 2006 184 Lecture 3 9 Coulomb s Law 1 10 2006 184 Lecture 3 10 Electric Force Coulomb s Law Consider two electric charges q1 and q2 The electric force F between these two charges separated by a distance r is given by Coulomb s Law kq1q2 F 2 r 9 The constant k is called Coulomb s constant and is given by 1 10 2006 2 k 8 99 10 Nm C 184 Lecture 3 2 11 Coulomb s Law 2 The coulomb constant is also written as 2 1 12 C k where 0 8 85 10 4 0 Nm 2 0 is the electric permittivity of vacuum A fundamental constant of nature 1 q1q2 F 1 10 2006 184 Lecture 3 4 0 r 2 12 Example What is the force between two charges of 1 C separated by 1 meter Answer 8 99 x 109 N i e huge 1 10 2006 184 Lecture 3 13 Electric Force The electric force is given by The electric force unlike the gravitational force can be positive or negative If the charges have opposite signs the force is negative Attractive If the charges have the same sign the force is positive Repulsive 1 10 2006 184 Lecture 3 q1q2 F k 2 r 14 Electric Force Vector Electric force in vector form q1 y r r1 q2 x r2 q1q2 F2 k 2 r r 1 10 2006 r r2 r1 r r r 2 1 r r r q1q2 F1 k 2 r r 184 Lecture 3 15 Superposition Principle The net force acting on any charge is the vector sum of the forces due to the remaining charges in the distribution F1 net F1 2 F1 3 F1 n F F F F 1n x 1x 12 x 13 x F1y F12 y F13 y F1n y F1z F12 z F13 z F1n z 1 10 2006 184 Lecture 3 16 Example The Helium Nucleus Part 1 The nucleus of a helium atom has two protons and two neutrons What is the magnitude of the electric force between the two protons in the helium nucleus Answer 58 N Part 2 What if the distance is doubled how will the force change Answer 14 5 N Inverse square law If the distance is doubled then the force is reduced by a factor of 4 1 10 2006 184 Lecture 3 17 Example Equilibrium Position Consider two charges located on the x axis x2 x1 The charges are described by q1 0 15 C x1 0 0 m q2 0 35 C x2 0 40 m Where do we need to put a third charge for that charge to be at an equilibrium point At the equilibrium point the forces from the two charges will cancel 1 10 2006 184 Lecture 3 18 Example Equilibrium Position 2 x1 x2 The equilibrium point must be along the x axis Three regions along the x axis where we might place our third charge x3 x1 x1 x3 x2 x3 x2 1 10 2006 184 Lecture 3 19 Example Equilibrium Position 3 x1 x2 x3 x1 Here the forces from q1 and q2 will always point in the same direction to the left for a positive test charge No equilibrium x2 x3 Here the forces from q1 and q2 will always point in the same direction to the right for a positive test charge No equilibrium 1 10 2006 184 Lecture 3 20 Example Equilibrium Position 4 x2 x1 q3 x1 x3 x2 Here the forces from q1 and q2 can balance q1q3 q2q3 k k 0 2 2 x3 x1 x2 x3 Check the signs 1 10 2006 Answer x3 0 16 m 184 Lecture 3 21 Example Charged Pendulums Consider two identical charged balls hanging from the ceiling by strings of equal length 1 5 m in equilibrium y Each ball has a charge of 25 C The balls hang at an angle 25 with respect to the vertical What is the mass of the balls x Ball on left 2 Step 1 Three forces act on each ball Coulomb force gravity and the tension of the string 1 10 2006 184 Lecture 3 kq Fx T sin 2 d Fy T cos mg 22 Example Charged Pendulums 2 Step 2 The balls are in equilibrium positions That means the sum of all forces acting on the ball is zero T sin kq2 d2 T cos mg 2 kq mg 2 d tan d 2 l sin Answer m 0 76 kg A similar analysis applies to the ball on the right 1 10 2006 184 Lecture 3 23 Electric Force and Gravitational Force Coulomb s Law that describes the electric force and Newton s gravitational law have a similar functional …
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