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# Download the electric field - IHS Physics Mr. Arnold

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Electric Fields 20.4-20.5 Questions If nothing existed to experience the gravitational field of Earth, would the field still exist? How do we describe the gravitational field of Earth? If we introduce an object to the gravitational field of Earth, how can we determine what force it will experience? Force Model vs. Field Model We have assumed that one charge exerts a force on another. However, in the field model, it is the alteration of space around one charge that is the agent that exerts the force on the second charge. The Force Model: One charge exerts a force directly on another force. The Field Model: One charge modifies the space around itself and the second charge responds to the altered space. The altered space is the agent that then exerts the force. The Electric Field A charge (or group of charges), known as the “source charges”, alter the space around them by creating an electric field. Free space has a constant value of the permittivity that appears in physical relationships. The permittivity of matter has a value different from that of free space. If another charge is placed in that electric field, it will experience a force exerted by the field. Field Models Electric Fields – alteration of space around a charge Gravitational Fields – alteration of space around a mass Magnetic Fields – alteration of space around a “magnet” Why use fields? Forces exist only when two or more particles are present. Fields exist even if no force is present. The field of one particle only can be calculated. Fields as a Ratio The force-to-charge ratio Fe E q Direction is defined as the direction of the force that a positive test charge will experience. The force-to-mass ratio g Fg m Direction is defined as the direction that a test mass will experience. Sample Problem The electric field in a given region is 4000 N/C pointed toward the north. What is the force exerted on a 400 μg styrofoam bead bearing 600 excess electrons when placed in the field? 3.84 x 10-13 N, south Sample Problem A 400 μg styrofoam bead has 600 excess electrons on its surface. What is the magnitude and direction of the electric field that will suspend the bead in midair? 4.08 x 1010 N, down Sample Problem A proton traveling at 440 m/s in the +x direction enters an electric field of magnitude 5400 N/C directed in the +y direction. Find the acceleration. 5.17 x 1011 m/s2, up Electrophoresis The DNA fragments are negatively charged because of the phosphate group. The electric field causes the force. ma F e FD qE FD a m The larger pieces of DNA have a smaller acceleration. Electric Field Diagrams Electric field vectors represent the electric field at a single point in space in proximity to a point charge. We always draw field vectors based on the force on a positive test (probe) charge. Electric Field Diagrams 1. 2. 3. 4. The electric field, a vector quantity, exists at every point in space. Electric field diagrams show a sample of the vectors, but there is an electric field vector at every point whether one is shown or not. The arrow indicates the direction and strength of the field at the point to which it is attached – at the point where the tail of the vector is placed. The length of any vector is significant only relative the lengths of other vectors. Although we have to draw vectors across the page, an electric field does not “stretch” from point to another. Each vector represents the electric field at one point in space. If the probe/test charge is positive, the electric force will point in the same direction as the electric field vector. If the probe/test charge is negative, the electric force will point in the opposite direction of the field vector. Electric Field Around a Positive Charge Electric Field Around a Negative Charge Spherical Electric Fields The Electric Field surrounding a point charge or a spherical charge can be calculated by: E 1 Q 40 r E: Electric Field (N/C) k: 8.99 x 109 N m2/C2 q: Charge (C) r: distance from center of charge q (m) Remember that k = 1/(4πε0) 2 kQ r 2 Sample Problem There is an isolated point charge of q = +15 μC in a vacuum. Determine the electric field at point P, which is 0.20 m away. Thought Experiment Imagine you have a small, positively charged pith ball hanging from a string. If you hang it at various locations between these two configurations of charged spheres, how will it behave? + + - + Superposition When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges. Again, as with force vectors, this is referred to as superposition. Sample Problem The figure shows two charged objects, A and B. Each contributes as follows to the net electric field at point P: EA=4.00 N/C directed to the right, and EB=3.00 N/C directed downward. Thus, EA and EB are perpendicular. What is the net electric field at P? Electric Dipoles Sample Problem A dipole consists of a positive and negative charge separated by 1.2 cm, as shown. What is the electric field strength at a point 1.2 cm to the right of the positive charge? Check Your Understanding A positive point charge +q is fixed in position at the center of a square, as the drawing shows. A second point charge is fixed to either corner B, corner C, or corner D. The net electric field at corner A is zero. (a) At which corner is the second charge located? (b) Is the second charge positive or negative? (c) Does the second charge have a greater, a smaller, or the same magnitude as the charge at the center?