# F = Q big = c) The electric potential in a certain region of space can be described by the equation: 16y2 (1 + z 2 ) V (x, y, z) = 10x

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1 1) Short Answer (4 points each)(show YOUR WORK) a) A 3.0 nc (positive) charge and a 1.0 nc (negative) charge are located 0.80 m apart from each other. What is the force on the 3.0 nc (positive) charge due to the 1.0 nc (negative) charge? F = b) Two widely separated spheres, one with a radius of 3.0 cm and charge on its outer surface q (Q small =q), and one sphere with a radius of 7.0 cm and no charge on its outer surface (Q big =q), are connected by a thin wire, i.e. the wire forces them to be at the same potential. The charge on the big (r=7.0 cm) sphere after the spheres are connected by a thin wire is: Q big = c) The electric potential in a certain region of space can be described by the equation: V (x, y, z) = 10x What is the electric field at the origin (0,0,0)? 16y2 (1 z 2 )

2 1) Short Answer (4 points each, cont d)(show YOUR WORK) d) Calculate the electric potential at point P for the collection of charges shown in the figure below. 10 nc P 1.0 cm 10 nc 10 nc 1.0 cm e) An isolated capacitor in air has a stored energy of J. If we now insert a dielectric material of dielectric constant κ = 1.3 into the gap of the capacitor, what is the new stored energy of the capacitor? U new =

3 2) Capacitors(Show your work)(4 pts. each part) Consider the circuit shown below. All capacitors are initially uncharged and both switches, S1 and S2, are open. We are going to close and open switches and calculate the outcome. V S1 C 1 C 2 A B S2 C 3 C 1 C 2 C 3 V = 10 pf = 20 pf = 30 pf a) We close only switch S1 and notice that a long time later (at electrostatic equilibrium) the charge on C 3 = 7.0pC. What is the potential difference of the battery? =? V batt = b) C 3 is a parallel plate capacitor with a an area of m 2. Calculate the magnitude of the electric field between the plates of of C 3, assuming the volume between the plates of C 3 is filled with a material of dielectric constant κ = 2. E batt =

4 2) Capacitors(cont d) c) How much energy is stored by capacitor C 1? U 1 = d) Find the effective capacitance between points A and B. C AB = e) Now switch S1 is opened and S2 is closed in that order: 1st: S1 opened 2nd: S2 closed After S2 is closed and the circuit has reached electrostatic equilibrium, calculate the potential difference across C 1. V new =

5 3) (Gauss Law) A conducting spherical shell, of inner radius a and outer radius b, is inside of and concentric with another conducting spherical shell, of inner radius c and outer radius d. The inner shell has a net charge of 2q and the outer shell has a net charge of q. A charge of 3q is located at the center of the 2 spheres at point P. U T R1 a b S c P d N R2 V M Charge at Center (P) = 3q inner shell net charge = 2q outer shell net charge = q Answer the following questions. (No need to show your work) a) What is the magnitude of the electric field at the point a/2, inside the spherical shells? (3 pts)

6 3) (Gauss Law)(No need to show your work)(cont d) b) What is the magnitude of the electric field at the point N, inside the inner shell? c) What is the magnitude of the electric field at R1, between the inner and outer shells? d) What is the magnitude of the electric field at point M, inside the outer shell? e) What is the magnitude of the electric field at R2, outside the outer shell? (3 pts) f) How much charge is on the inside surface (surface S) of the inner sphere? Charge = g) How much charge is on the outside surface (surface T) of the inner sphere? Charge = h) How much charge is on the inside surface (surface U) of the outer sphere? Charge = i) How much charge is on the outside surface (surface V) of the outer sphere? Charge =

7 4) Electric Fields (Vectors)(show your work ) Two infinite lines of charge, one with charge/length, λ, of 1.0µC/m and the with a charge/length, λ, of 1.0µC/m are placed as shown: the negative line of charge at (-d,d) and the positive line of charge at (-d,-d). (assume d = 20 cm and that all lines of charge are absolutely parallel) λ y d x d λ d P(0,0) λ = 1.0µC/m d = 20 cm a) What is the magnitude and direction of the electric field at the point P (0,0)? (5 pts. each) E X = E Y =

8 4) Electric Fields (cont d) b) Where should a third positive line of charge with charge/length, λ, be placed so that the total electric field vanishes (equals zero) at point P? (5 pts. each) X = Y =

9 5) Electric Fields (Position, Velocity, Acceleration)(show some work please) Two large parallel copper plates are 2.0 cm apart and have a uniform electric field of magnitude N/C between them as depicted below. An electron is released from the negative plate at the same time that a proton is released from the positive plate. Neglect the force of the particles on each other and gravity. e 2.0 cm p E = N/C a) Find the distance from the positive plate when they pass each other.(10 pts.) Distance = b) How fast is the electron moving when they pass each other. (5 pts.) V elocity = c) How much work did it take to accelerate the electron to this velocity? (5 pts.) W ork =

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