PES 1120 Spring 2014, Spendier Lecture 3/Page 1. Last time we used Coulomb's law to calculate the electric force between point charges

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1 PES 110 Spring 014, Spendier Lecture 3/Page 1 Lecture today: Chapter 1 1) Coulomb's law: D example ) Charge is quantized 3) Charge is conserved Last time we used Coulomb's law to calculate the electric force between point charges magnitude: F k q q 1 r1 q 1 - Charge in Coulombs of first object [C] q - Charge in Coulombs of second object [C] r 1 - separation distance [m] k - Electrostatic Constant, k = 8.99 x 10 9 Nm /C q1q vector form: F k rˆ ˆr... unit vector r If the particles have the same signs of charge, the force on particle 1 is in the direction of ˆr ; if they have opposite signs, the force is opposite ˆr.

2 PES 110 Spring 014, Spendier Lecture 3/Page Example 1: Three point charges are held in the triangular shape shown. What is the net electric force and direction on q?

3 PES 110 Spring 014, Spendier Lecture 3/Page 3 Example : Three point charges are held in the triangular shape shown. In which direction will q move? Here we had three charges, 75 μc, 75 μc and 50 μc. But what is the minimum charge we can consider?

4 PES 110 Spring 014, Spendier Lecture 3/Page 4 Charge is quantized: We already mentioned that there is a so called elementary charge. It is the magnitude of charge on the electron (and proton). The unit of charge that is called the Coulomb (C). Every proton has charge: +e = x C "e" stands for electron Every electron has charge: -e = x C While some fundamental particles have charges that are fractions of this unit, one cannot isolate these fundamental particles in nature (only in big particle colliders, initial evidence in 1968). For example protons and neutrons are composed of even smaller particles called quarks: up (/3 e), charm (/3 e), top (/3 e), down (-1/3 e), strange (-1/3 e), bottom (-1/3 e). A proton, composed of two up quarks and one down quark. In this class we will not worry about fundamental particles that have charges that are fractions of e since the cannot be isolated in nature. For this and for historical reasons, we do take the magnitude of charge on the electron (and proton) to be the elementary charge. All objects have charge: q = ne = n (1.60 x C), where n is an integer: n = +/- 1, +/-, +/- 3,..., When a physical quantity such as charge can have only discrete values rather than any value, we say that the quantity, like charge, is quantized. It is possible, for example, to find a particle that has no charge at all (neutron) or a charge of +10e or -6e, but not a particle with a charge of, say, 3.57e Example 3: What charge in C does a Nitrogen atom have when it is stripped of 3 electrons? Answer: Nitrogen has 7 protons, 7 neutrons, and 7 electrons. Stripped 3 electrons, hence only 4 electrons left: q = +7e (-4e) = + 3e = 3 (1.60 x C) = x C Example 4: A plastic sheet has an area of 50 cm and charge of -1.5 x 10-6 C. a) How many electrons does this charge correspond to? b) What is the charge density on the surface of the plastic sheet? a) q = n(-e) n = q/e = -1.5 x 10-6 C/(-1.60 x C) = 9.4 x 10 1 ( sig figs, no units) b) charge density = σ = charge/area = -1.5 x 10-6 C/ (0.5 m ) = -3.0 x 10-6 C/m

5 PES 110 Spring 014, Spendier Lecture 3/Page 5 Charge is conserved This means if you start with a neutral object one can only give it a net positive or negative charge by either taking charge from it or putting charge on it from some other object. Charges move between objects. Charge cannot be created nor destroyed. Example - rubbing piece of rubber on fur In both cases the total charge (on the rod and the fur) is zero. What happened is that the charge redistributed itself. Example 5: Initially, sphere A has a charge of -10e and sphere B has a charge of +0e. The spheres are made of conducting material and are identical in size. a) If the spheres then touch, what is the resulting charge on sphere A? b) How many electrons moved in order to equalize the charge distribution? Radioactive Decay Important examples of the conservation of charge occur in the radioactive decay of nuclei, in which a nucleus transforms into (becomes) a different type of nucleus. In this case, the sum of charges of the initial state of the decay has to equal the had the sum of charges in the final state of the decay.