Exam 1PHY20619-29-05Name:_______________________ ___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 12Sphere: 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� 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 =PHY20619-29-05Name:_______________________ ___1. [6 points] A central particle of charge 2q is surrounded by a square array of chargedparticles. The length of the square side is d, and charges are placed at the square corners, at the midpoint of the sides, and midway between the corner and the midpoint for two sides. What are the magnitude and direction of the net electrostatic force on the central particle due to the other particles?Page 2 of 12+2q 7q +4q5q 3q+3q 2q 3q d3q 5q+4q 7q +2qPHY20619-29-05Name:_______________________ ___2. [6 points] Particles 1, with a charge q1 , and 2, with a charge q2, are on the x-axis with particle 1 at x = 2a and particle 2 at x = a. For the net force on a third charged particle placed at the origin to be zero, what must be q2 in terms of q1 ? Page 3 of 12PHY20619-29-05Name:_______________________ ___3. Consider electric charge distributed along a one-dimensional path in the form shown as ¾ of a circle. The circle is centered at the origin with a radius of R, and the linear charge density is positive. (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 4 of 12yxRPHY20619-29-05Name:_______________________ ___4. [8 points] In the figure shown, a small, non-conducting ball of mass 63 10 kgm-= � and charge 4.8 Cq m=+ (distributed uniformly through its volume) hangs from an insulating thread that makes an angle with a vertical, uniformly charged non-conducting sheet (shown in cross section). The sheet has a surface charge density of11 23 10 C/ms-= �. Considering the gravitational force of the ball and assuming that the sheet extends far vertically and into and out of the page, calculate the angle .Page 5 of 12PHY20619-29-05Name:_______________________ ___5. Consider a cube with side length s = 0.5 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( )3ˆ ˆ ˆ2 4 6 N/Cy z= + +E x y z?(b) [6 points] What is the electric charge density (C/m3) at the center of the top face at y = 0.5 m if the electric field is the same as in part (a)?Page 6 of 12yxzPHY20619-29-05Name:_______________________ ___6.(a) [6 points] A solid non-conducting sphere of radius 0.05 mR =has a uniform charge density30.01 C/mr = constant throughout the volume of the sphere. What is the ratioof the magnitude of the electric field at / 2r R= to that at r R=?(b) [6 points] Suppose the solid non-conducting sphere in part (a) has a non-uniform charge density( )40 0, where 0.267 C/mr rr r r= = (i.e. varies with radius). What is the ratio of the magnitude of the electric field at / 2r R= to that at r R=?Page 7 of 12PHY20619-29-05Name:_______________________ ___7. Three charged, concentric, spherical conducting shells have radii1 2 310 cm, 15 cm, 20 cmR R R= = =. The thickness of the conducting shells, while not zero, is considered negligible. The charge on the innermost shell is 15C, the charge on the middle shell is 20C, and the charge on the outermost shell is +25C.(a) [6 points] What is the charge on the inner surface of the outermost conducting shell?(b) [6 points] What is the direction and magnitude of the electric field at radius17 cmr =?Page 8 of 12R1R2R3PHY20619-29-05Name:_______________________ ___8. [8 points] A proton is injected with a velocity of 62 10 m/sv = �into a region of uniform electric field between two large plates separated by 1m and maintained with an electric potential difference of 30,000 V. The proton travels from lower electric potential to higher on a path perpendicular to the plates. Does the proton reach the far plate, and if not, what is the distance of closest approach to it? The charge of the proton is 191.6 10 Ce-+ = �, and the proton mass is 271.67 10 kgpm-= �.Page 9 of 12v+++++++EpPHY20619-29-05Name:_______________________ ___9. [6 points] The electric potential along the x-axis (in kV=103 V ) is plotted versus the value of x (in meters). Evaluate the x-component of the electrical force (in Newtons) on a charge of 4.70 C located on the x-axis at x= 1.2 m.Page 10 of 12PHY20619-29-05Name:_______________________ ___10.(a) [6 points] Consider the shown arrangements of capacitors above. Calculate the effective capacitance,effC, of the network between the terminals A and B given that each of the shown capacitors has a capacitance C = 4 F.(b) [6 points] Consider the above infinite chain of capacitors. Calculate the effective capacitance, effC, of the network between the terminals A and B given that each of the shown capacitors has a capacitance C = 4 F.Page 11 of 12ABAB PHY20619-29-05Name:_______________________ ___11. [6 points] A parallel plate capacitor with a capacitance of 12 F is connected to a battery that maintains an electric potential difference of 6V. If the plates are squeezedto one-third of
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