# 1. Short Answer (25 points total)

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2 1. Short Answer (25 points total) a) (4 points) Describe, briefly, the electric field at the points indicated on the figure to the right. Each horizontal line represents an infinite sheet of charge with identical positive charge density. A +σ +σ A B C B C b) (2 points) A constant Electric field is pointing in the direction indicated in the figure. Please draw an arrow to indicate the direction of INCREASING electric potential (V). E c) (2 points) Circle the combination of capacitors with the largest capacitance between the two ends (labeled a & b for each combination). a b a b d) (3 points) If I held a positively charged plastic wand next to a soda can that is lying on its side on a flat table, and the can is uncharged, would the soda can be attracted to, or repelled by, the soda can? Also, indicate on the figure, the arrangement of the free charge in the soda can after the charged wand is brought near. (hint: we did this in class)

3 1. Short Answer (Continued) e) (2 points) At Electrostatic Equilibrium (when charges stop moving around), the electric field inside a conductor is: SMALL LARGE f) (2 points) If I lift my pen up, I m the gravitational potential energy of the pen. INCREASING DECREASING g) (2 points) The Electric flux through a closed (or complete) surface (sometimes called a closed, Gaussian surface) is proportional to the charge the closed surface. INSIDE OUTSIDE h) (2 points) The Electric Potential (V) inside a conductor at Electrostatic Equilibrium is best described as: ZERO CONSTANT i) (2 points) If I insert a dielectric material of dielectric constant K > 1 between the plates of a capacitor that had only air between the plates before (I.e. K = 1 before, K > 1 after), the capacitance of the capacitor. INCREASES DECREASES j) (2 points) Two charges, each of value +Q are arranged as shown in the figure below. At which location, P1 or P2, is the electric potential the largest? (See figure below) +Q P1 P2 +Q k) (2 points) If 2 conducting spheres are connected by a wire so that they are at the same potential, which of the spheres would you expect to have the greatest electric field at its surface? (assume there is some charge on the combination) THE SMALLER SPHERE THE BIGGER SPHERE

4 2) Various Subjects (5 points each) (Circle the Correct Response, Show work for Partial Credit): 1) A +4.0 C (positive) charge and a -2.0 C (negative) charge are located 0.50 m apart from each other. What is the force on the +4.0 C (positive) charge due to the -2.0 C (negative) charge?(5 pts.) I) 7: N and repulsive II) 7: N and attractive III) 1: N and repulsive IV) 2: N and attractive V) 2: N and repulsive 2) Two widely separated spheres, one with a radius of 1.0 cm and charge on its outer surface +q (Q small =+q), and one sphere with a radius of 10.0 cm and no charge on its outer surface (Q big =0), are connected by a thin wire, i.e. the wire forces them to be at the same potential. The charge on the big (r=10.0 cm) sphere af ter the spheres are connected by a thin wire is:(5 pts.) I) Q big =0:50 q II) Q big =0:01 q III) Q big =1:0 q IV) Q big =0:91 q V) Q big =1:1 q 3) If a10:0 kg particle with charge 3:0 C is placed in an electric field,!e =2:0 (N=C) ^x, and then released, how fast is the particle moving after 5:0 s?(at t =0theparticle is at rest)(5 pts.) I) v =3:0 m=s II) v =9:0 m=s III) v =15m=s IV) v =33m=s V) v =0:33 m=s

5 2) Various Subjects (Continued) +2.0 C P 0.5m 0.5m 0.5m -2.0 C -2.0 C 4) What is the electric potential at point P for the three charges in the figure, each of which is placed at one point of an equilateral triangle?(5 pts.) I) V =0:0 Volts II) V = 3: Volts III) V = 7: Volts IV) V = 1: Volts V) V = 1: Volts 5) What is the gap between the plates of a parallel plate capacitor in air if the Area of the gap is 0:5 m 2 and the capacitance is 2: F?(5 pts.) I) 1: cm II) 0:58 cm III) 0:14 cm IV) 1:8 cm V) 7:1 cm

6 3) Electric Field Vectors (25 points total) Consider the charges arranged at the corners of a square as shown in the figure below. +2Q -Q y d P x Q = 2.0 uc d = 10 cm -2Q d +Q a) Calculate the x and y components of the electric field at the point indicated by P. E x = (10) E y = (10) b) Suppose we have a cube that encloses all 4 of the charges. (I.e. we put the charges in a box.) What is the total electric flux through the surface of the entire cube? Φ tot = (5)

7 4) Capacitors in a circuit (25 points total) Consider the circuit shown below: The battery has been hooked up for a long time. All the charge has stopped moving around. The circuit has reached its equilibrium state. Please answer the following questions: V + C 3 C C 1 2 C 1 C 2 C 3 = 10 pf = 20 pf = 30 pf V = 6.0 Volts a) What is the charge on C 3? Q = (8) b) What is the potential difference across C 1? V = (4)

8 c) What is the charge on C 2? Q = (3) d) What is the total energy stored in the capacitors? U = (5) e) A material of dielectric constant K (K > 1) is inserted between the plates of C 2. Circle the correct answer below (there may be more than 1). The potential difference across each capacitor behaves as follows.(5 pts.) I) C 1 goes up III) C 2 goes up V) C 3 goes up II) C 1 goes down IV) C 2 goes down VI) C 3 goes down

9 5) Electric Potential (25 points total) A conducting spherical shell of inner radius R1 and outer radius R2 has a charge of +Q placed at its center andacharge -4Q placed on it (this means that the sum of the charge on the inner surface of the conductor and the outer surface of the conductor is equal to -4Q). (see the figure below). Briefly explain your reasoning and show your work R Q R Q The electric potential V is zero at radius of r = 1. Please find the algebraic expression for the electric potential in all regions of space. Inside the Shell: V = r<r1 (10) Inside the Conductor: R1 <r<r2 V = (10) Outside the Shell: V = r>r2 (5)

10 Equations! F 12 = 1 4ßffl 0 q 1 q 2 r 2 12 ^r 12 (Point Charge)! E =! F =q test = 1 4ßffl 0 q r 2 12 ^r 12 Φ= I!E d! A = I!E ^nda = q enclosed ffl 0 ; Φ = E A (special cases) (Sphere) A =4ßr 2 ; (Cylinder) A =2ßrL; (Sheet) A = L 2 + L 2 (two sides)! F = m! a ; x = x 0 + v 0x t a xt 2 ; v x = v 0x + a x t Z!F U = W = d! 1 s ; Kinetic Energy = 2 mv2! X!! X! X F total = Fi E total = E i V total = Q = CV; U = 1 2 CV 2 = 1 2 i i Q 2 C ; C = C 0; E = E 0 ; ffl = ffl 0 i V i Z F! (V F V I )= E d! s ; I E ; E ; E ; C = ffl 0A d C = Parallel Plate 2ßffl 0L ln(b=a) Cylindrical ab C =4ßffl 0 a b Spherical (series)1=c equiv =1=C 1 +1=C 2 + :::; (parallel)c equiv = C 1 + C 2 + ::: Constants ffl 0 = 8: F 12 C2 ffl m 0 = 8:85 10 Nm 2 e = 1: C M electron = 9: kg M proton = 1: kg k = 1 4ßffl 0

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