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Electric Fields March 13-15 Today • HW Tonight - Online (Electrostatics Problems 2.5) > Net Charge; Coulomb's Law • Tomorrow - Short Quiz: Charges, Coulomb's Law • Electric Fields > see Notes online: Intro to Electrostatics CP Physics 1 Electric Fields March 13-15 Question: Why does the Electrostatic Force have the characteristics that we observe? E.g., why does the Force increase as Q increases? Why does the Force vary inversely with distance? Answer: Michael Faraday's ELECTRIC FIELD CP Physics 2 Electric Fields March 13-15 Classical Definition: If a small positive "test" charge q0 is placed at a point in space, and it is observed to experience an Electrostatic Force FE, then at that there exists an Electric Field, E, such that E = FE q0 The direction of the Electric Field is defined as the direction of the Electrostatic Force on the positive charge. > This implies that a positive charge will experience an FE in the same direction as E; a negative charge will experience an FE in the opposite direction as E. The unit for Electric Field is N/C. CP Physics 3 Electric Fields March 13-15 Example 1: A proton is observed to experience an Electrostatic Force to your left; the force has a magnitude of 4.8 E-15 N. What is the magnitude and direction of the Electric Field at the location of this proton? Example 2: An electron is placed in a uniform Electric Field, with a magnitude of 5 E5 N/C, and it is directed downwards. What is the magnitude and direction of the Electrostatic Force on this electron? CP Physics 4 Electric Fields March 13-15 Electric Field Lines We can represent the Electric Field in diagrams with arrows (pointing in the direction of E). The relative strength of the Electric Field will be shown by the density of the Field lines (i.e., how closely spaced they are); the closer together the lines, the stronger the field at that point. lines spaced far apart will indicate a weak E field here, the tightly packed lines represent a strong E field Notice the field lines are parallel and equally spaced; this implies that the E field in this region is Uniform (constant) If you were to put a small positive charge (red circle) in this E field, it will feel a Force in the direction of the field (green arrow). A small negative charge (purple circle) would feel a force opposite the direction of the field (black arrow). CP Physics 5 Electric Fields March 13-15 Electric Field Due to a "Point" Charge: For a given charge Q that is at a point in space, it is surrounded by a spherical Electric Field. The magnitude of this field depends on the size of the charge, and the distance from the charge. We can calculate this Electric Field as E = kQ R2 where k = 9 E9 Nm2/C2, and R is the distance from the charge. • Note: this can be derived from Coulomb's Law CP Physics 6 Electric Fields March 13-15 Example 1: What is the magnitude and direction of the Electric field a distance of 0.25 m from a Van de Graaff generator dome that has a net charge of -8 E-6 C? Example 2: What is the strength of the Electric field a distance of 3 E-10 m from a Carbon nucleus, which contains 6 protons and 6 neutrons? What is the Electrostatic Force on an electron located at that point? Example 3: A balloon is rubbed on a wool sweater, and a detector measures an Electric field with a magnitude of 270 N/C when placed a distance of 0.10 m from the balloon. What is the amount of net charge on the balloon? What is the number of charges associated with this net charge? CP Physics 7 Electric Fields March 13-15 E-field due to Q: Diagrams We can represent the Electric field around a charge Q with a diagram, integrating the concepts of Electric Field Lines. The E-field vectors will be drawn according to a few basic rules: 1. E-field vectors point away from a positive charge and towards a negative charge; 2. E-field lines/vectors can NEVER touch or cross each other; 3. The number of E-field lines indicate the size of the charge (more lines = stronger field). Why? CP Physics 1. Recall that the direction of the E-field is the direction of the force on a positive charge. A + charge will be repelled from a + charge (so Efields go away from +), and attracted to a - charge (so E-fields go towards a - charge). 2. If the E-field lines touch/cross, that implies that a charge at a certain point in space could feel a force in multiple directions; this is impossible, as the force is always parallel to the E-field. 3. Recall that the density of the E-field lines indicates its magnitude; if you draw more lines around a charge, this requires the lines to be more densely packed, indicating a stronger E-field. 8 Electric Fields March 13-15 E-field Diagrams + E-field near a Positive charge - E-field near a Negative charge Notice in the diagrams above: • When you are close to the charge (R is small) the E-field lines are close together (indicating a stronger field ⇒ stronger Force) • As you get farther away from the charge, the lines spread out (weaker field ⇒ weaker Force) > This is why the Force is stronger when charges are closer together; the Fields have a greater magnitude when you are near the charge • The number of E-field lines in the diagram above indicate the amount of charge; more lines = more charge CP Physics 9 Electric Fields March 13-15 What if there are multiple charges? We can diagram any Electric Field, for any number of charges, by using the rules that govern E-fields and E-field lines: 1. Away from +, Towards - 2. E-field lines point in the direction of the Force on a + test charge 3. The density of the lines indicates the relative strength of E 4. The number of lines indicates the relative size of the charge For multiple charges, we end up with E-fields that contain lines that curve and bend as a result of the sum of two Force vectors. Some examples are shown below: Electric Dipole: + and - charge of equal size; arrows indicate the direction of E. Note that, for all points equidistant from the + and -, the E-field is Horizontal, from + to -. two + charges of equal size. Notice that, at the center, E = 0! Also, for all points on the vertical line that bisects the charges, the E-field is vertical (excluding the exact center point). The diagram is identical for - charges, except the arrows point to the charges CP Physics 10 Electric Fields CP Physics March 13-15 11