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Circuits (MTE 120) (Spring 2010) Akrem El-ghazal http://pami.uwaterloo.ca/~akrem/ University of Waterloo, Electrical and Computer Engineering Dep. Electric Fields Objectives: 1. To define and learn some aspects of electric field. 2. To learn how to compute the electric field. Electric Fields: Q (charge) creates an electric field (E) around it and E exerts force (F) on any other charge in the field. Therefore, E is the transition from charge to electric force. The Electric Field Due to a Point Charge Suppose, there is a test charge (=q0) beside charge q .The magnitude of the electric field at point p is: || | | || 1 x | | The unit of electric field is || . The direction of the electric field is same as the direction of the force. It is along the line connecting the charge to the point p. Note Electric field exists independently of the test charge. The Test charge is used only for definition. Example: Electric field could be zero at a point. Circuits (MTE 120) (Spring 2010) Electric Field Lines: • The Electric field lines provide a way to visualize the patterns in the electric field. • The electric field lines emanate from positive charge and terminate on a negative charge. • No two field lines can cross. • The tangent to the electric field lines at any point gives the direction of E at that point. • The number of field lines per unit area, measured in a plane that is perpendicular to the lines, is proportional to the magnitude of E (more field lines perpendicular to the area means stronger E). Electric field Lines for positive charge Electric field Lines for negative charge Electric field Lines for a positive point charge and nearby a negative point charge that are equal in magnitude. Electric field Lines for two positive point charges that are equal in magnitude 2 Circuits (MTE 120) (Spring 2010) For infinitely large sheet + + + ++ + + + + + + + + + + + E Electric field Lines of an infinitely large sheet with a uniform distribution of positive charge The Principle of Superposition If we have multiple charges, we calculate the field by the principle of superposition. If we place a positive test charge q0 near n point charges q1,q2,..qn then the net electrostatic force acting on the test charge due to the n point charges is : . . . Therefore, the net electric field E at the position of the test charges is Example: … For the following charges find the net electric field Enet at the origin. 3 Circuits (MTE 120) (Spring 2010) Solution Step # 1: Calculate the magnitude of the electric field (| 1|, | 2| and 3 ) created by each charge: |2| |2| |4| , Step #2: Identify the direction of each electric field at the origin using a positive test charge. Since 1 and 2 have the same direction, their sum vector has that direction and a magnitude: 2 2 4 2 " 3 , we realize that the equal y components From the symmetry of the two vectors! 1 of the two vectors cancel and the equal x component add. Therefore, the net field at the origin is in the positive direction of the x axis and has the magnitude: 4 4 8 $% cos)30+ cos)30+ cos)30+ 6.93 / 4