2212_Test2-1 - PHYS 2212 Test 2 Spring 2011 Name(print Instructions • Read all problems carefully before attempting to solve them • Your work

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PHYS 2212 Test 2 Spring 2011 Name(print) Instructions • Read all problems carefully before attempting to solve them. • Your work must be legible, and the organization must be clear. • You must show all work, including correct vector notation. • Correct answers without adequate explanation will be counted wrong. • Incorrect work or explanations mixed in with correct work will be counted wrong. Cross out anything you don’t want us to read! • Make explanations correct but brief. You do not need to write a lot of prose. • Include diagrams! • Show what goes into a calculation, not just the final number, e.g.: 5 × 104 a·b c·d = (8×10−3 )(5×106 ) (2×10−5 )(4×104 ) = • Give standard SI units with your results. Unless specifically asked to derive a result, you may start from the formulas given on the formula sheet, including equations corresponding to the fundamental concepts. If a formula you need is not given, you must derive it. If you cannot do some portion of a problem, invent a symbol for the quantity you can’t calculate (explain that you are doing this), and use it to do the rest of the problem. Honor Pledge “In accordance with the Georgia Tech Honor Code, I have neither given nor received unauthorized aid on this test.” Sign your name on the line above PHYS 2212 Do not write on this page! Problem Problem Problem Problem Problem Score 1 2 3 4 (25 (25 (25 (25 pts) pts) pts) pts) Grader Problem 1 (25 Points) Consider a very thin glass rod bent into a half-circular arc that has uniform charge Q and radius R. Answer the following questions to determine the electric field at a point on the z-axis. (a 5pts) Consider an infinitesimal slice of the bent rod with angular length dθ located at an angle θ from the right end of the rod as indicated in the figure. Find the position vector r that points from center of this slice to the observation location A =< 0, 0, L > on the z-axis. (b 5pts) Determine an expression for the charge of the slice, dQ, in terms of the infinitesimal angular length dθ and relevant known variables. (c 10pts) Derive an expression for the vector electric field dE of the slice of the rod at the observation location A in terms of the given variables and known constants. (d 5pts) Integrate over the charge distribution to determine the electric field E at observation location A. You answer should only contain the given variables and known constants. Problem 2 (25 Points) An isolated large-plate capacitor (not connected to anything) originally has a potential difference of 500 volts with an air gap of 6 mm. Then a plastic slab 2 mm thick, with dielectric constant 4, is inserted into the air gap as shown in the diagram. (a 2pts) Draw the orientation of the induced dipoles in the plastic slab. (b 5pts) Draw three arrows representing the net electric field in the three regions inside the capacitor. Recall that longer arrows mean larger magnitudes. For the plastic slab, draw the average electric field. (c 5pts) Determine the potential difference V1 − V2 . Be sure to show all of your work (d 5pts) Determine the potential difference V2 − V3 . Be sure to show all of your work (e 5pts) Determine the potential difference V3 − V4 . Be sure to show all of your work (f 3pts) Determine the potential difference V4 − V1 . Be sure to show all of your work Problem 3 (25 Points) A thin spherical shell made of plastic carries a uniformly distributed negative charge −Q1 . Two large thin disks made of glass carry uniformly distributed positive and negative charges +Q2 and −Q2 . The radius of the plastic spherical shell is R1 and the radius of the glass disks is R2 . Note that the diagram is not drawn to scale and R1 << R2 (i. e. the disks make up a capacitor). Calculate the potential difference V3 − V2 . Problem 4 (25 Points) N y A straight wire 15 m long (the rest of the circuit is not shown here) oriented along the y axis, lies below a compass as shown. The wire is much longer than is shown here and the diagram is not to scale. The compass is centered on the origin and is 4 mm above the wire. When a conventional current of I amperes flows through the wire, the compass deflects 8◦ to the west. x (a 5pts) On the diagram draw the direction of the conventional current I in the wire. Briefly explain how you determined this. (b 15pts) Determine the magnitude of the conventional current I flowing through the wire and be sure to show all of your work. (c 5pts) With the current still running in the straight wire, a current carrying loop is placed near the compass, and the compass now deflects 16◦ to the west. Which of the diagrams below indicates where the loop was placed? The directions indicated in the diagrams below refer to the conventional current. Circle the diagram of your choice . Your answer must be consistent with part (a). N N (a) (b) y y conventional current flows clockwise, viewed from top of ring conventional current flows clockwise, viewed from top of ring x (c) x (d) y y N N x conventional current flows clockwise, viewed from right of ring x conventional current flows counter-clockwise, viewed from right of ring This page is for extra work, if needed. Things you must know Relationship between electric field and electric force Electric field of a point charge Relationship between magnetic field and magnetic force Magnetic field of a moving point charge Conservation of charge The Superposition Principle Other Fundamental Concepts dp dp = Fnet and ≈ ma if v << c dt dt f ∆V = − i E • dl ≈ − (Ex ∆x + Ey ∆y + Ez ∆z ) Φmag = B • ndA ˆ dv dt ∆Uel = q ∆V Φel = E • ndA ˆ qinside E • ndA = ˆ a= 0 |emf| = EN C • dl = B • ndA = 0 ˆ dΦmag dt Iinside path + B • dl = µ0 B • dl = µ0 0 d dt Iinside path E • ndA ˆ Specific Results 1 2qs (on axis, r s) 4π 0 r 3 Q 1 (r ⊥ from center) Erod = 4π 0 r r 2 + (L/2)2 1 2Q/L Erod ≈ (if r L) 4π 0 r z Q/A (z along axis) 1− 2 Edisk = 20 (z + R2 )1/2 Q/A (+Q and −Q disks) Ecapacitor ≈ Edipole,axis ≈ 0 µ0 I ∆ × r ˆ ∆B = (short wire) 2 4π r µ0 µ0 2I LI Bwire = ≈ (r 2 + (L/2)2 4π r r 4π r 1 −qa⊥ 4π 0 c2 r i = nAv ¯ Erad = σ = |q | nu Edielectric = Eapplied K 1 qs (on ⊥ axis, r 4π 0 r 3 s) electric dipole moment p = qs, p = α Eapplied qz 1 (z along axis) 2 + R2 )3/2 4π 0 (z Q/A Q/A z Edisk ≈ ≈ (if z R) 1− 20 R 20 Q/A s just outside capacitor Ef ringe ≈ 2R 0 Ering = ∆F = I ∆l × B L) µ0 2IπR2 2IπR2 µ0 ≈ (on axis, z 4π (z 2 + R2 )3/2 4π z 3 µ0 2µ Bdipole,axis ≈ (on axis, r s) 4π r 3 Bloop = Edipole,⊥ ≈ Bwire = Bearth tan θ R) µ = IA = IπR2 Bdipole,⊥ ≈ µ0 µ (on ⊥ axis, r 4π r 3 ˆ ˆ v = Erad × Brad ˆ Brad = I = |q | nAv ¯ I J= = σE A 1 q 1 ∆V = − 4π 0 rf ri v = uE ¯ L R= σA due to a point charge s) Erad c I= | ∆V | for an ohmic resistor (R independent of ∆V ); R Q = C |∆V | power = I ∆V Power = I ∆V K ≈ 1 mv 2 if v 2 c I= circular motion: dp |v | mv 2 = |p| ≈ dt ⊥ R R |∆V | (ohmic resistor) R Math Help a × b = ax , ay , az × bx , by , bz = (ay bz − az by )ˆ − (ax bz − az bx )ˆ + (ax by − ay bx )ˆ x y z dx = ln (a + x) + c x+a dx 1 =− +c 2 (x + a) a+x a dx = ax + c Constant Speed of light Gravitational constant Approx. grav field near Earth’s surface Electron mass Proton mass Neutron mass Electric constant Epsilon-zero Magnetic constant Mu-zero Proton charge Electron volt Avogadro’s number Atomic radius Proton radius E to ionize air BEarth (horizontal component) ax dx = Symbol c G g me mp mn 1 4π 0 0 µ0 4π µ0 e 1 eV NA Ra Rp Eionize BEarth a2 x +c 2 dx 1 =− +c 3 (a + x) 2(a + x)2 ax2 dx = a3 x +c 3 Approximate Value 3 × 108 m/s 6.7 × 10−11 N · m2 /kg2 9.8 N/kg 9 × 10−31 kg 1.7 × 10−27 kg 1.7 × 10−27 kg 9 × 109 N · m2 /C2 8.85 × 10−12 (N · m2 /C2 )−1 1 × 10−7 T · m/A 4π × 10−7 T · m/A 1.6 × 10−19 C 1.6 × 10−19 J 6.02 × 1023 molecules/mole ≈ 1 × 10−10 m ≈ 1 × 10−15 m ≈ 3 × 106 V/m ≈ 2 × 10−5 T ...
View Full Document

This note was uploaded on 05/23/2011 for the course PHYISCS 2212 taught by Professor Shatz during the Spring '10 term at Georgia Institute of Technology.

Ask a homework question - tutors are online