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Chapter 19 Electric Charges, Forces, and Fields (Cont.) Dr. Jie Zou PHY 1161 1 Outline Superposition of electric forces Electric field Electric field of a point charge Superposition of electric fields Electric field lines Dr. Jie Zou PHY 1161 2 Superposition of forces Dr. Jie Zou When a charge experiences forces due to two or more other charges, the net force on it is simply the vector sum of the forces taken individually. Superposition of forces: F1 F12 F13 F14 PHY 1161 3 Example 19-3: superposition Three charges, each equal to +2.90 C, are placed at three corners of a square 0.500 m on a side, as shown in the diagram. Find the magnitude and direction of the net force on charge number 3. Dr. Jie Zou PHY 1161 4 The electric field Definition of the electric field F q0 q0 is a test charge and F is the electric force exerted on q0 by the electric field. Vector quantity E The electric force and the electric field: F qE A positive charge experiences a force in the same direction of E . A negative charge experiences a force in the opposite direction of E . Dr. Jie Zou PHY 1161 “Force field” associated with charge q 5 Example 19-4: force field In a certain region of space, a uniform electric field has a magnitude of 4.60x104 N/C and points in the positive x direction. Find the magnitude and direction of the force this field exerts on a charge of (a) +2.80 C and (b) -9.30 C. Dr. Jie Zou PHY 1161 6 Electric field of a point charge Magnitude of the electric field due to a point charge: q Ek 2 r Direction of the electric field of a point charge If the charge q is “+”, its field points radially outward. If the charge q is “-”, its field points radially inward. Dr. Jie Zou PHY 1161 7 Superposition of electric fields The electric field due to a system of charges can be found by superposition. The total electric field is found by calculating the vector sum of the electric fields due to each charge separately. Dr. Jie Zou PHY 1161 8 Example 19-5: Superposition in the Field In the figure, q1=q2=+2.90 C. The square has a size of 0.500 m on each side. Find the magnitude and direction of the net electric field at point 3. Dr. Jie Zou PHY 1161 9 Electric Field Lines Electric field lines: Imagined pictorial representation of the electric field. Rules for drawing electric field lines Point in the direction of the electric field vector at every point. Start at positive (+) charges or at infinity. End at negative (-) charges or at infinity. Are more dense where the electric field has a greater magnitude. The number of lines entering or leaving a charge is proportional to the magnitude of the charge. Dr. Jie Zou PHY 1161 10 More Examples An electric dipole Dr. Jie Zou PHY 1161 Uniform electric field produced by a parallel-plate capacitor 11 Homework #1 Chapter 19, P. 684-685, Problems: #31, 35, 48 (from Walker, 4th ed.) Dr. Jie Zou PHY 1161 12