Physics Pre lab 212P 2 Electric Fields and Superposition Name Section Date Read this answer the questions before coming to lab Summary of relevant concepts a The electric field at any point in space is defined as the force experienced by a test charge of 1 C Hence the magnitude of the electric field at a distance r from a SINGLE point charge Q is given by Coulomb s Law Q E k 2 where k 8 99 x 109 N m2 C2 r b The electric field from a COLLECTION of POINT charges is given by the vector sum of the electric fields from all the individual point charges superposition c Electric field lines provide a convenient way of visualizing the electric field in any region of space Electric field lines originate at positive charges and terminate at negative charges The electric field at any given position is tangential to the electric field line The spacing between electric field lines is inversely proportional to the strength of the electric field i e they are closer together where the field is stronger and further apart where the field is weaker d A common arrangement of charges in Nature is the electric dipole This consists of two charges equal in magnitude Q but of opposite sign separated by a distance a An electric dipole is characterized by the dipole moment p Qa This is a vector that points from the negative charge towards the positive charge Pre lab Questions Q1 An important principle that you learnt about in lecture is superposition The use of superposition depends on a clear understanding of vector sums What is the vector sum of the three vectors shown below They all have the same magnitude 1200 1200 1200 Magnitude of resultant vector Direction of resultant vector Q2 The figure below shows 4 positive charges of equal magnitude arranged on a semicircle centered about the origin What is the direction of the net electric field produced at the origin Direction of electric field y 450 450 x Now use superposition to calculate the direction and magnitude of the electric field at a point P that lies on the perpendicular bisector of an electric dipole See figure below Your goal is to first determine the electric field at any general value of r and then in the limit r a P r Q Q a Q3 In the diagram above draw vectors that represent the electric field produced at P by each charge Also draw a vector that represents the net electric field produced by the sum of these two vectors Q4 From the vector diagram that you used above derive an exact expression for the magnitude of the electric field at P The only parameters in your final expression should be the dipole moment p Qa the distance r the distance a and the constant k from Coulomb s Law Call this expression Equation 1 You will need it in the lab activity Q5 Simplify your analytical expression for E r for large distances i e r a You should obtain a particularly simple expression Call this expression Equation 2 Needed later in lab activity Q6 A rule of thumb calculation no calculators Suppose you are at some distance r from an electric dipole such that r is much larger than the dipole separation a You measure the magnitude of the electric field from the dipole to be 0 001 N C If you double your distance from the dipole approximately what is the magnitude of the electric field