Exam 1PHY20619-28-06Name:_______________________ ___Exam 1Closed book exam. A calculator is allowed, as is one 8.511” sheet of paper with your own written notes. Please show all work leading to your answer to receive full credit. Numerical answers should be calculated to 2 significant digits. Exam is worth 100 points, 25% of your total grade.UF Honor Code: “On my honor, I have neither given nor received unauthorized aid in doing this exam.”Page 1 of 10Sphere: 2 344 3.14159273S r V rp p p= = =e 16022 1019. Cx x y y z za b a b a b�= + +a b( )( )( )y z y z x z x z x y x ya b b a a b b a a b b a� = - - - + -a b x y z9 2 2019 10 N m / C4Kpe= = �12 2 208.8542 10 C / N me-= � c 3 0 108. m/s1 2122ˆq qKr=F r0q=FEenc0ESqdeF = � =�Ε Α�0re�� =E V=- �E0UVq=CW U d=- D = ��F sCV dD =- ��E sˆ ˆˆx y zx y z� � ��= + +� � � ( )yxzFFFdivx y z����� = = + +� � �F F V SdV d�� = �� �F FΑ� eff 1 2R R R= +eff 1 21 1 1R R R= +Q C V= D( )2212 2QU C VC= D =eff 1 2C C C= +eff 1 21 1 1C C C= +61 C 10 Cm-=61 F 10 Fm-=121 pF 10 F-=191 eV 1.6 10 J-= �212K mv=242b b acxa- � -=29.8 m/sg =LRAr=dqidt= V iRD =PHY20619-28-06Name:_______________________ ___1. A central particle of charge 3q is surrounded by a hexagonal array of other charged particles (q>0). The length of a side is s, and charges are placed at each corner. (a) [6 points] Find the component of the force along the x-axis (Fx) on the central particle.(b) [6 points] Find the component of the force along the y-axis (Fy) on the central particle.Page 2 of 10 +4q +2q +2q +2q 2q 3q 2qsxyPHY20619-28-06Name:_______________________ ___2. Consider electric charge distributed along a one-dimensional path in the form shown as two sections of ¼ of a circle each. The circle is centered at the origin with a radiusof R, and the linear charge density is + in the left quadrant and in the right. (a) [6 points] Find the component of the electric field along the x-axis (Ex) at the origin (0,0).(b) [6 points] Find the component of the electric field along the y-axis (Ey) at the origin (0,0). Page 3 of 10yxR+PHY20619-28-06Name:_______________________ ___3. Consider a cube with side length s = 2 m and one corner at the origin (0,0,0) as shown.(a) [6 points] What is the total charge enclosed by the cube if the electric field is( )2ˆ ˆˆ3 5 2 N/Cx z= + -E i j k?(b) [6 points] What is the electric charge density (C/m3) at the center of the right face at x = 2 m if the electric field is the same as in part (a)?Page 4 of 10yxzPHY20619-28-06Name:_______________________ ___4. [8 points] A flat nonconducting surface infinite in extent carries a uniform charge density of 9 23 10 C/ms-= �. A small circular hole of radius 1.5 mR =has been cut in the middle of the sheet as shown. Calculate the electric field at a point z = 5 m away from the center of the hole along an axis perpendicular to the surface. (In other words, consider z R?, but don’t set /R zexactly equal to zero. You may find the superposition principle useful.)Page 5 of 10zRPHY20619-28-06Name:_______________________ ___5. [8 points] An electron is launched away from the surface of an infinite nonconducting sheet of charge with a velocity of 62 10 m/sv = �on a trajectory perpendicular to the surface. The charge density of the sheet is 5s =+ nC/m2. Is the electron able to reach a distance infinitely far away from the charged sheet, and if not,how far does it travel before turning around? The charge of the electron is191.6 10 Cq e-=- =- �, and the electron mass is 319.11 10 kgem-= �.Page 6 of 10v+++++++PHY20619-28-06Name:_______________________ ___6. A conducting sphere of radius R1 contains a charge Q. It is surrounded by a concentricspherical conducting shell of radius R2 > R1 and charge Q. (a) [6 points] What is the difference in electric potential between the shell and the sphere?(b) [6 points] What is the capacitance of the arrangement of conductors?Page 7 of 10PHY20619-28-06Name:_______________________ ___7. [6 points] Initially two electrons are fixed in place with a separation of 2.15 µm. Howmuch work must be done to bring a third electron in from infinity to complete an equilateral triangle?8. [6 points] Sketch the electric field lines for a negatively charged particle above the surface of a flat perfectly conducting surface (both above and below the surface).Page 8 of 10conductorPHY20619-28-06Name:_______________________ ___9. A 1.5 µF capacitor is charged to a potential difference of 12 V, and the charging battery is disconnected. (a) [6 points] What is the energy stored in the capacitor?(b) [6 points] If the charged capacitor is then connected in parallel with a second (initially uncharged) capacitor, and if the potential difference across the first capacitorsubsequently drops to 9 V, what is the capacitance of this second capacitor?Page 9 of 10PHY20619-28-06Name:_______________________ ___10. [6 points] The electric potential along the x-axis (in V) is plotted versus the value of x, (in cm). Evaluate the x-component of the electrical force (in Newtons, including sign) on a proton located on the x-axis at x = 10 cm.11. [6 points] Two wires are made out of the same material (copper). One has a circular cross section with radius r = 1 mm and a length of 10 cm, the other has a square crosssection with width s = 1 mm and a length of 5 cm. Which wire has the larger resistance?Page 10 of
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