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## Electric Fields

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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. • Ifanother 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.**The force-to-charge ratio**The force-to-mass ratio Fields as a Ratio Direction is defined as the direction of the force that a positive test charge will experience. 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. 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**• 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.**Spherical Electric Fields**• The Electric Field surrounding a point charge or a spherical charge can be calculated by: • 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)**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?**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?