Physics 2102 Jonathan Dowling Physics 2102 Final Exam Review A few concepts electric force field and potential Electric force What is the force on a charge produced by other charges What is the force on a charge when immersed in an electric field Electric field What is the electric field produced by a system of charges Several point charges or a continuous distribution Electric potential What is the potential produced by a system of charges Several point charges or a continuous distribution Plus a few other items Electric field lines equipotential surfaces lines go from ve to ve charges lines are perpendicular to equipotentials lines and equipotentials never cross each other Gauss law q 0 Given the field what is the charge enclosed Given the charges what is the flux Use it to deduce formulas for electric field Electric dipoles field and potential produced BY a dipole torque ON a dipole by an electric field potential energy of a dipole Electric potential work and potential energy work to bring a charge somewhere is W qV signs Potential energy of a system negative work done to build it Conductors field and potential inside conductors and on the surface Shell theorem systems with spherical symmetry can be thought of as a single point charge but how much charge Symmetry and infinite systems Conductors and insulators Will two charged objects attract or repel Can a charged object attract or repel an uncharged object What is the electric field inside a conductor What is the direction of the electric field on the surface of a conductor What happens to a conductor when it is immersed in an electric field Electric forces and fields point charges Figure 22N 14 shows an arrangement of four charged particles with angle 34 and distance d 2 20 cm The two negatively charged particles on the y axis are electrons that are fixed in place the particle at the right has a charge q2 5e a Find distance D such that the net force on the particle at the left due to the three other particles is zero b If the two electrons were moved further from the x axis would the required value of D be greater than less than or the same as in part a Other possible questions what s the electric field produced by the charges XXX at point PPP what s the electric potential produced by the charges XXX at point PPP What s the potential energy of this system Electric dipoles What s the electric field at the center of the dipole On axis On the bisector far away What is the force on a dipole in a uniform field What is the torque on a dipole in a uniform field What is the potential energy of a dipole in a uniform field Electric fields of distributed charges Possible problems questions What s the electric field at the center of a charged circle What s the electric field at the center of of a charged circle What s the electric field far from the ring far from the disk What s the electric field of an infinite disk Gauss law A long non conducting solid cylinder of radius 4 1 cm has a nonuniform volume charge density that is a function of the radial distance r from the axis of the cylinder as given by Ar2 with A 2 3 C m5 a What is the magnitude of the electric field at a radial distance of 3 1 cm from the axis of the cylinder b What is the magnitude of the electric field at a radial distance of 5 1 cm from the axis of the cylinder Gauss law At each point on the surface of the cube shown in Fig 24 26 the electric field is in the z direction The length of each edge of the cube is 2 3 m On the top surface of the cube E 38 k N C and on the bottom face of the cube E 11 k N C Determine the net charge contained within the cube 2 29e 09 C Gauss law applications Electric potential electric potential energy work In Fig 25 39 point P is at the center of the rectangle With V 0 at infinity what is the net electric potential in terms of q d at P due to the six charged particles The figure shows conducting plates with area A 1m 2 and the potential on each plate Assume you are far from the edges of the plates What is the electric field between the plates in each case What and where is the charge density on the plates in case 1 What happens to an electron released midway between the plates in case 1 Derive an expression in terms of q2 a for the work required to set up the fourcharge configuration of Fig 25 50 assuming the charges are initially infinitely far apart The electric potential at points in an xy plane is given by V 2 0 V m2 x2 4 0 V m2 y2 What are the magnitude and direction of the electric field at point 3 0 m 3 0 m Questions from checkpoints and questions in the textbook U 5U0 7U0 3U0 5U0 Problem Calculate electric field at point P x P dx L Field very far away a E Potential of Continuous Charge Distribution Uniformly charged rod Total charge Q Length L What is V at position P shown x P dx L a Q L dq dx L kdq k dx V r L a x 0 k ln L a x L 0 L a V k ln a Problem Field at center of arc Line Of Charge Field on bisector dE P Distance Charge per unit length k dq dE 2 d a d dx x o L q L d a 2 x 2 Q k dx a dE y dE cos 2 a x 2 3 2 a cos 2 2 1 2 a x Line Of Charge Field on bisector L 2 L 2 dx x E y k a 2 2 3 2 k a 2 2 2 a x a x a L 2 L 2 2k L 2 2 a 4a L What is E very far away from the line L a Ey 2k L a 2a k L a2 kq a2 What is E if the line is infinitely long L a 2k L 2k Ey 2 a a L Problem Gauss Law to Find E Gauss Law Cylindrical Symmetry Approximate as infinitely long line E radiates outwards Choose cylindrical surface of radius R length L co axial with line of charge E 1m E A E 2 RL q L 0 0 L E 2k 2 0RL 2 0R R R 1 mm Potential Energy of a System of Charges Potential Energy of A System of Charges 4 point charges each Q are connected by strings forming a square of side L If all four strings suddenly snap what is the kinetic energy of each charge when they are very far apart Use conservation of energy Final kinetic energy …
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