1. Two point charges are fixed on the y-axis: a negative point charge q1= -25C at y1= +.22 m and a positive point charge q2 at y2= +.39 m. A third point charge q3= 8.4C is fixed at the origin. The net electrostatic force exerted on the charge q3 has a magnitude of 27N in the positive y direction.A) What is the charge on q2? B) Suppose q2 is moved to another system, where q2 is at x= +3 m and another charge, q4, which has a charge of +2q2, is located at the origin, where along the x-axis does the electric field equal 0? 2. A hollow conducting shell with inner radius of 1.5 m and an outer radius of 2.2 m; the shell has a total charge of +12C. If the inner surface has an induced charge of +4C when a point charge is placed inside A) What is the charge of the point charge? B) What is the induced charge on the outer surface? C) What is the average volume charge density at a (i) radius=1.1 m and (ii) radius=2.5 m3. A particle (charge of -20C) is released from rest into a uniform electric field of +150 N/C in the +y direction. The particle has a mass of 3.2 kg. A) What is the force (magnitude and direction) on the particle? B) After 10s, what is the velocity (magnitude and direction) of the particle? C) If the particle suddenly came to a stop by an outside force, what is the potential difference across the initial point where the force was applied and the particles final position? No energy is lost to heat.4. An electric field points along the y-axis, E= (300 y N/C)j. A box is constrained by the following constraints: ; ; A) What is the charge within the box? B) What is the electric potential difference between the point (y,z)= (1,6) and (8,8)? C) What is the electric potential difference between the point (y,z)= (1,1) and (1,1)?5. An electric dipole consists of +Q and Q (|Q|= 6.0C) and they are separated by 72 cm. It is within an electric field of 1.8 and the Electric field points along x. A) What is the torque on the dipole when it is perpendicular to the field? B) What is the torque on the dipole when it is at a 45? C) What is the change in potential energy within the system when it finishes rotating?

1. There is a point charge q1 = + 10 C, located at the origin of a coordinate system, and a second charge q2 = + 40 C, located at x = 6.0 m, away. a. Where does the electric field due to the charges vanish? b. Sketch the electric field lines. c. How much energy was needed to bring these charges together to where they are (assume they were originally separated by an infinite distance)? 2. A uniformly-charged cylinder has a radius RC = 0.5 m and charge density =4/ C/m3 . a. What is its charge per unit length? b. If a point charge q = - 5.0 C is placed a distance r = 2 m from its center, what is the electrostatic force on that charge? 3. A conducting spherical shell of inner radius a = 0.8 m and outer radius b = 1.0 m carries a charge of QC = -20 C. A uniformly-charged sphere of radius RS = 2.0 cm and charge QS = + 15 C is placed in the center of the shell. a. Find the electric field everywhere (including direction) as a function of the radial distance r from the center. What are the charges on the b. inner and c. outer surfaces of the shell? d. What is the electric potential (relative to infinity) on the outer surface of the shell? 4. There is an electric field E~ = (500y N/C)j pointing along the yaxis. a. Given a box located in coordinates (in meters) 2.0 x 4.0 0 y 3.0 0 z 4.0, How much charge is contained in the box? (You may leave your answer in terms of 0.) b. What is the electric potential difference between the points (x, y) = (2.0,2.0) and (3.0,5.0), in the x-y plane?1. Qi on a tiny sphere, a portionqis transferred to 2nd, nearby sphere. Both spheres can be treated as particles. For what value ofq/Qwill the electrostatic force between the two spheres be maximized?2. Particle 1 of charge +qand particle 2 of charge+4.00qare held at a separationL=3.90cm on anx-axis. (a) the ratioq3/q? (b) thex&y-coordinates of particle 3?3. Particle 1 of charge +4eis above a floor by distanced1=2.80mm and particle 2 of charge +6eis on the floor, at distanced2=5.60mm horizontally from particle 1. What is thexcomponent of the electrostatic force on particle 2 due to particle 1?4. How far apart must two protons be if the magnitude of the electrostatic force acting on either one due to the other is equal to the magnitude of the gravitational force on a proton at Earths surface?5. What are the (a) magnitude and (b) direction of the net electrostatic force on particle 4 due to the other three particles? All four particles are fixed in thexyplane, andq1=-8.0010-19C,q2=+4.8010-19C,q3=+8.0010-19C,q4= +3.2010-19C,1=20.0,d1= 3.00 cm, andd2=d3= 2.00 cm6. What is the magnitude of a point charge whose electric field78cm away has the magnitude1.5N/C?7. In the figure, the four particles form a square of edge lengtha=4.00cm and have chargesq1=+20.0nC,q2=-40.0nC,q3=+40.0nC andq4=-20.0nC. What net electric field do the particles produce at the square's center?8. Nonconducting rod of lengthL=5.50cm has charge -q=-4.60fC uniformly distributed along its length.(a) What is the linear charge density of the rod? (b) What is the magnitude of the electric field at pointP, a distancea= 12.0 cm from the end of the rod? (c) What is its direction? (d) What is the electric field magnitude produced at distancea= 50 m by the rod?9. A charged cloud system produces an electric field in the air near the Earth's surface. A particle of charge-2.810-9C is acted on by a downward electrostatic force of 3.010-6N when placed in this field. (a) What is the magnitude of the electric field?(b) What are the magnitude and direction of the electrostatic forceFelexerted on a proton placed in this field?(c) What is the magnitude of the gravitational forceFgon the proton?(d) What is the ratioFel/Fgin this case?10. Beams of high-speed protons can be produced in "guns" using electric fields to accelerate the protons. (a) What acceleration would a proton experience if the gun's electric field were1.20104N/C?(b) What speed would the proton attain if the field accelerated the proton through a distance of1.40cm?11. It is found experimentally that the electric field in a certain region of Earth's atmosphere is directed vertically down. At an altitude of210m the field has magnitude 60.0 N/C. At an altitude of150m, the magnitude is 100 N/C. Find the net amount of charge contained in a cube60m on edge, with horizontal faces at altitudes of150and210m. Neglect the curvature of Earth. 12. An infinite line of charge produces a field of magnitude4.70104N/C at a distance of1.8m. Calculate the linear charge density.13. A square plate of edge length12.0cm and negligible thickness has a total charge of6.9010-6C. (a) Estimate the magnitudeEof the electric field just off the center of the plate (at, say, a distance of 0.50 mm from the center) by assuming that the charge is spread uniformly over the two faces of the plate. (b) EstimateEat a distance of41m (large relative to the plate size) by assuming that the plate is a point charge.14. An unknown charge sits on a conducting solid sphere of radius9.0cm. If the electric field14cm from the center of the sphere has magnitude3.1103N/C and is directed radially inward, what is the net charge on the sphere?15. The electric field at pointPjust outside the outer surface of a hollow spherical conductor of inner radius 10 cm and outer radius 20 cm has magnitude460N/C and is directed outward. When an unknown point chargeQis introduced into the center of the sphere, the electric field atPis still directed outward but is now165N/C. (a) What is the net charge on and enclosed by the outer spherical surface beforeQis introduced? (b) What is chargeQ? (c) AfterQis introduced, what is the charge on the inner surface of the conductor? (d) What is it on the outer surface?16. A spherical drop of water carrying a charge of35pC has a potential of580V at its surface (withV= 0 at infinity). (a) What is the radius of the drop?(b) If two such drops of the same charge and radius combine to form a single spherical drop, what is the potential at the surface of the new drop?17. Two metal spheres, each of radius5.0cm, have a center-to-center separation of1.1m. Sphere 1 has charge+2.8010-8C. Sphere 2 has charge of3.2010-8C. Assume that the separation is large enough for us to assume that the charge on each sphere is uniformly distributed (the spheres do not affect each other). TakeV= 0 at infinity. Calculate the potential: (a) at the point halfway between the centers. (b) on the surface of sphere 1. (c) on the surface of sphere 2.18. A long, solid, conducting cylinder has a radius of 2.0 cm. The electric field at the surface of the cylinder is175N/C, directed radially outward. LetA,B, andCbe points that are 1.0 cm, 2.0 cm, and9.0cm, respectively, from the central axis of the cylinder. (a) What is the magnitude of the electric field atC? (b) What is the electric potential differenceVB-VC? (c) What is the electric potential differenceVA-VB?19. A uniform charge of+14.0C is on a thin circular ring lying in anxyplane and centered on the origin. The ring's radius is 3.00 cm. If pointAis at the origin and pointBis on thezaxis atz=3.70cm, what isVB-VA?20. A spherical conducting shell has a charge of-16C on its outer surface and a charged particle in its hollow. (a) If the net charge on the shell is-12C, what is the charge on the inner surface of the shell? (b) If the net charge on the shell is-12C, what is the charge of the particle?