Introduction to Electromagnetism - 3

Three charges on a line Three charges in a plane Point Charge The term point charge refers to a particle of zero size that carries an electric charge The electrical behavior of electrons and protons is well described by modeling them as point charges NEXT Electric Fields due to particular Charge Distributions Electric Dipole (polar molecule) Charged Rod Uniform Ring of Charge Uniformly Charged Disk Biological Examples DNA structure and replication DNA (which passes on genetic information) is made up of 4 bases adenine (A), cytosine , guanine (G) and thymine (T) All living cells posses some sort on electrostatic field that can interact with other cells and molecules Click to edit Master title style Click to edit Master text styles Second level Third level Fourth level Fifth level Instructor Franco Gaspari PHY 1040U (Physics for the biosciences) Introduction to Electromagnetism and Optics Lecture 3 January 16, 2007 Determine the magnitude and direction of the net electrostatic force on q1 0.20 m 0.15 m q2 q1 q3 q1 q2 q3 r12 0.15 m r13 0.10 m 73o Determine the magnitude and direction of the net electrostatic force on q1 All charges have magnitude q, red negative, blue positive. Rank the arrangements in descending order according to the magnitude of the net electrostatic force on the positive charge. The force between two charged bodies, q1 and q2 is a force at a distance Review Q Why does one charge feel the other charge A A charged body creates an Electric Field around itself ke 8.987 x 109 Nm2/C2 o Permittivity of free space We could say that when a body, A, is charged, the space around it is changed and it is very different from what it was before the charging The space around the charge acquires electric properties (forces) that did not exist before The charge qA of A generates an electric field in the surrounding space. We also say that a region of space is the site of an electric field if, by placing a charged body C at any point in the region, we see that the body is subject to some (electrostatic) force It we make the charge C a very small one, q0, we call it a test (or point) charge M1 mo A large sphere of mass M1 is placed on an elastic trampoline, thus creating a curvature (a trough). A smaller sphere of mass mo will move along the curvature. To an external observer from the top it will seem that mo is attracted by the large sphere. By convention, the test charge is positive. q1 q2 q3 q4 q0 We put a positive test charge, q0, at point P and we measure the force, F, experienced by the charge. Then we divide the vector F by the value q0. E F/q0 (N/C) Analog to g F/m Definition of the electric field E Example of a simple electric field Q -Q q0 q0 Consider the electric field generated by a charge Q, either positive (I) or negative (II). E is independent of q0. It is a property of a point in space regardless Of the presence of another charge What happens when we have more that one charge generating the electric field We know that in the case of 2 charges acting on a third charge at point P, we can calculate the resulting force on the third charge by doing a vector sum of the individual Coulomb Forces FP F1 F2 Therefore, if the third charge is our test charge qo, we can derive the electric field there EP FP/qo (F1 F2)/qo F1/qo F2/qo E1 E2 The electric field is the vectorial sum of the single electric fields The electric field depends only on the charges that generate it and the point where it is measured Therefore, if we know the electric field at a point P, we can calculate the electrostatic Force at that particular point for any charge q, i.e. F q E FP F1 F2 The electric field due to 2 charges Q1 Q2 q q j E1 E2 E2y E2x 2d Let us calculate the electric field along the x axis. -q The double Helix note the AT and CG pairings Close up view. The electrostatic force is significant only when the pairs are close enough so that, for example, the H atom of adenine is attracted to the O- atom of thymine - Suppose we have Cl-, Na , and Ca2 ions, as shown below, in an aqueous solution (dielectric constant k 80.4). Find the electric force on the Na ion due to the other two ions. Cl- Na Ca2