Physics 2102 Gabriela Gonz lez Charles Augustin de Coulomb 1736 1806 Summary of last lecture Electric field is a vector calculated the electric force on an imaginary 1C positive charge Electric field lines start or end in electric charges When fields are strong electric field lines get closer Electric field of a single charge is E kq r2 The dipole moment vector p has magnitude qa and direction from ve to ve charge Far from a dipole E kp r3 p http phet colorado edu en simulation electric hockey 1 Thus far we have only dealt with discrete point charges In general a charged object has a continuous charge distributed on a line a surface or a volume How do we calculate the electric field produced by such an object Approach divide the continuous charge distribution into infinitesimally small elements Treat each element as a POINT charge compute its electric field Sum integrate over all elements Always look for symmetry to simplify life Q L Useful idea charge density Line of charge charge per unit length Sheet of charge charge per unit area Volume of charge charge per unit volume Q A Q V 2 Uniform line of charge Q spread over length L What is the direction of the electric field at a point P on the perpendicular bisector a Field is 0 b Along y c Along x Choose symmetrically located elements of length dx x components of E cancel P y a x dx o dx Q L y Figure shows a uniformly charged rod of charge Q bent into a circular arc of radius R centered at 0 0 What is the direction of the electric field at the origin x a Field is 0 Choose symmetric elements b Along y x components cancel c Along y 3 Uniform line of charge length L total charge Q Compute explicitly the magnitude of E at point P on perpendicular bisector Showed earlier that the net field at P is in the y direction let s now compute this P y a x o Q L Distance dE P Charge per unit length a d dx x o Q L 4 What is the field E very far away from the line L a Far away any localized charge looks like a point charge What is field E if the line is infinitely long L a Q L is infinite This is not a physical situation it is an approximation for when we are very close to the charged line and then it looks infinite Figure shows a uniformly charged rod of charge Q bent into a circular arc of radius R centered at 0 0 Compute the direction magnitude of E at the origin y 450 x y dQ Rd d x 2Q R 5 Electric field lines and forces The drawings below represent electric field lines a Draw vectors representing the electric force on an electron at point A and on a proton at point B b If the magnitude of the force on an electron at A in a is 1 5 N what is the electric field at point B in each case We work with two different kinds of problems easily confused Given certain electric charges we calculate the electric field produced by those charges Example we calculated the electric field produced by the two charges in a dipole Given an electric field we calculate the forces applied by this electric field on charges that come into the field Example forces on a single charge when immersed in the field of a dipole another example force on a dipole when immersed in a uniform field 6 Net force on dipole 0 center of mass stays where it is Net TORQUE INTO page Dipole rotates to line up in direction of E 2 QE a 2 sin Qa E sin p E sin p x E The dipole tends to align itself with the field lines What happens if the field is NOT UNIFORM Distance between charges a Q Uniform Field E Q QE QE 7
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