3. A solid conducting sphere has net charge of +6nC. At electrostatic equilibrium the electric field inside the sphere is:

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1 Conceptual Questions. Circle the best answer. (2 points each) 1. If more electric field lines point into a balloon than come out of it, you can conclude that this balloon must contain more positive charge than negative charge. A) TRUE B) FALSE 2. A solid non-conducting sphere has a uniform charge density and a net charge of +6nC. At electrostatic equilibrium the electric field inside the sphere is: a) zero b) varies with 1/r c) varies with 1/ r 2 d) varies with r e) varies with r 2 3. A solid conducting sphere has net charge of +6nC. At electrostatic equilibrium the electric field inside the sphere is: a) zero b) varies with 1/r c) varies with 1/ r 2 d) varies with r e) varies with r 2 4. An uncharged spherical conducting shell surrounds a q point charge at the center of the shell. Then charge on the outside of the shell. When static equilibrium is reached, the charges on the inner and outer surfaces of the shell are respectively. a. q, 0. b. 2 q, q. c. 2 q, 3q. d. q, q. e. q, 2q. 5.A dipole is placed near to a point charge Q. The net force on this dipole is zero because the dipole is neutral. a. True b. False q is placed 6. If a box contains equal numbers of protons and electrons, the electric flux through this box will be zero only when the charges are all at its center. A True B. False 7. Metal spheres 1 and 2 are touching. Both are initially neutral. a. The positively charged rod is brought near. b. The spheres are separated. c. The positively charged rod is then removed. Afterward, the charges on the sphere are: A. Q 1 is + and Q 2 is +. B. Q 1 is + and Q 2 is. B. Q 1 is and Q 2 is +. C. Q 1 is and Q 2 is. D. Q 1 is 0 and Q 2 is A particle with a charge +Q is inside a spherical Gaussian surface, and three other charges (one with a charge +Q and two with a charge -Q) are outside the Gaussian surface, as shown. The net electric flux through the surface is A) greater than zero (flowing out of the sphere). B) less than zero (flowing into the sphere). C) equal to zero. 9. The equation for the electric field of an object with a net charge Q can be expressed using E=kQ/r 2 A) if an only if the object is a point charge (like an electron or proton). B) if the object is stationary. C) if the object is either a point charge or the object is a uniformly charged sphere and r is greater than its radius. D) if the object is a sphere, a disk, or a ring. E) regardless of the shape of the object. 10. An electron is initially moving to the right when it enters a uniform electric field directed upwards, as shown in the figure. Which trajectory (X, Y, Z, or W) will the electron follow in the field? A) trajectory W B) trajectory X C) trajectory Y D) trajectory Z

2 Problems (16 points each) Show all your work. Box your final answers using 3 sig figs. 1. If a = 60 cm, b = 80 cm, Q = 6.0 nc, and q = 6.0 nc, what is the magnitude and direction of the electric field at point P in the figure? Show the E Field vectors due to q and Q and the resultant E field vector. You can draw it in the diagram. Label it too.

3 2. The figure shows two parallel plates that are 2.00 cm apart. The electric field between them is N/C. An electron is launched at a 45.0 angle and with initial speed v o from the positive plate. What is the maximum v o such that the electron won't hit the negative plate?

4 3. Charge of uniform density σ 1 =40 pc/m 2 is distributed on a spherical surface (R 1 = 1.0 cm), and a second concentric spherical surface (R 2 = 3.0 cm) carries a uniform charge density σ 2 = 60 pc/m 2. What is the magnitude of the electric field at a point r = 4.0 cm from the center of the two surfaces? Use Gauss s Law to DERIVE an expression for the E field as a function of r in terms of the given variables R 1, R 2, σ 1, σ 2, r and constants. Simplify it. Box it. Then put in the numbers and get a numerical value to 3 sig figs. Show how the units work out. Box it.

5 4. A long non-conducting cylinder (R = 6.0 mm) has a non-uniform volume charge density given by ρ = r 2, where = 6.2 mc/m 5 and r is the distance from the axis of the cylinder. What is the magnitude of the electric field at a point 2.0 mm from the axis? Use Gauss s Law to DERIVE an expression for the E field as a function of r in terms of the variables ρ, r, R and constants (may include all or not). Make sure it is simplified. Box it. Then put in the numbers and get a numerical value to 3 sig figs. Show how the units work out. Box it.

6 5. Two uniform rods, each of length 2.0 m, are bent to form semicircles. One rod has a charge per unit length of 1.5 nc/m, and the other has a charge per unit length of 1.5 nc/m. The semicircles are joined to make a circle. What is the magnitude of the electric field at the center of the circle? Use Coulomb s Law to DERIVE an expression for the E field. Justify the steps. Box it. Then put in the numbers and get a numerical value to 3 sig figs. Show how the units work out. Box it. (Hint: Symmetry arguments can help simplify!)