77777 77777Instructor: P. KumarPHYSICS DEPARTMENTPHY 2049 Exam I May 30, 2008Name (print, last first): Signature:On my honor, I have neither given nor received unauthorized aid on this examination.YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP OF EACH PAGE.DIRECTIONS(1) Code your test number on your green answer sheet (use 76–80 for the 5-digit number). Code your nameon your answer sheet. Darken circles completely (errors can occur if too light). Code your student number onyour answer sheet.(2) Blacken the circle of your intended answer completely, using a number 2 pencil . Do not make any straymarks or the answer sheet may not read properly.(3) The answers are rounded off. Choose the closest to exact. There is no penalty for guessing.>>>>>>>>WHEN YOU FINISH <<<<<<<<Hand in the green answer sheet separately.1. Two identical conducting spheres A and B carry equal charge. They are separated by a distance much larger than theirdiameters. A third identical conducting sphere C is uncharged. Sphere C is first touched to A, then to B, and thenremoved. Finally, spheres A and B are brought into contact and then separated. As a result, the electrostatic forcebetween A and B, which was originally F, becomes:(1) 25F/64 (2) F/2 (3) F/4 (4) 5F/8 (5) 3F/82. A particle with charge 3µC is placed at the origin, an identical particle, with the same charge, is placed 2m from theorigin on the x axis, and a third identical particle, with the same charge, is placed 2m from the origin on the y axis.The magnitude of the force on the particle at the origin is:(1) 2 .9 × 10−2N (2) 1 .4 × 10−2N (3) 2 .0 × 10−2N (4) 4.0 × 10−2N (5) 8 .1 × 10−2N3. A charged oil drop with a mass of 2 × 10−4kg is held suspended by a downward electric field of 300N/C. The charge onthe drop is:(1) −6.5 × 10−6C (2) −1.5 × 10−6C (3) +6.5 × 10−6C (4) +1.5 × 10−6C (5) 04. Positive charge +Q is uniformly distributed on the upper half a semi-circular rod (from North to West to South) and negative charge –Q isuniformly distributed on the lower half. What is the direction of theelectric field at point P, the center of the semicircle? (North is up)(1) South (2) North (3) West (4) East (5) North-East5. Choose the INCORRECT statement:(1) According to Gauss’ law, if a closed surface encloses no charge, then the electric field must vanish everywhere on thesurface.(2) Gauss’ law states that the net number of lines crossing any closed surface in an outward direction is proportional tothe net charge enclosed within the surface.(3) Coulomb’s law can be derived from Gauss’ law and symmetry.(4) Gauss’ law applies to a closed surface of any shape.(5) Gauss’ law can be derived from Coulomb’s law.77777 777776. Positive charge Q is placed on a conducting spherical shell with inner radius R1and outer radius R2. A particle withcharge q is placed at the center of the cavity. The magnitude of the electric field at a point in the cavity, a distance rfrom the center, is:(1) zero (2) kq/r2(3) kQ/R21(4) k(q + Q)/r2(5) k(q + Q)/(R21− r2)7. The electric potential at points in an xy plane is given by V = (3.0V/m2)x2− (4.0V/m2)y2. What is the electric Fieldat the point (3.0 m, 3.0 m) (Ex, Eyin V/m)?(1) ( −18, 24) (2) (18, −24) (3) (27, −36) (4) (−27, 36) (5) none of these8. In the rectangle shown, the sides have lengths 5 cm and 15 cm, q1=−7.5C, and q2= +2.5C. How much work (in joules) is required tomove a third charge q3= +2.5C from A to B along a diagonal of therectangle?(1) −3.0 × 1012J (2) − 1.2 × 1012J (3) − 4.2 × 1012J (4) 9.0 × 1012J (5) none of these9. An air filled parallel plate capacitor has a capacitance of 4µF. If the separation between the plates is decreased by afactor of 2 and a material with a dielectric constant of 12 (like Silicon) is inserted between the parallel plates, what isthe new capacitance, in units of µF?(1) 96 (2) 48 (3) 4 (4) 24 (5) 0.6710. Capacitor C1is connected alone to a battery and charged until themagnitude of the charge on each plate is 4.0 × 10−8C. Then it isremoved from the battery and connected to two other capacitors C2and C3, as shown. The charge on the positive plate of C1is then1.0 × 10−8C. The charges on the positive plates of C2and C3are:C1C3C2(1) q2= 3.0 × 10−8C and q3= 3.0 × 10−8C(2) q2= 2.0 × 10−8C and q3= 2.0 × 10−8C(3) q2= 5.0 × 10−8C and q3= 1.0 × 10−8C(4) q2= 3.0 × 10−8C and q3= 1.0 × 10−8C(5) q2= 1.0 × 10−8C and q3= 3.0 × 10−8C11. Charges are arranged on a square of side d as shown in the diagram. In what directionis the electric field at the center of the square?x+3Q+Q+Q −5Q+3Q−Q−5Q−2Q(1) Fourth quadrant (2) First quadrant (3) Second quadrant (4) Third quadrant (5) E = 012. Refer to the previous problem. What is the potential at the center of the square (in units of kQ/d), assuming V = 0 atinfinity?(1) −7.7 (2) +1 .3 (3) −9.5 (4) −0.50 (5) +0THE FOLLOWING QUESTIONS, NUMBERED IN THE ORDER OF THEIR APPEARANCE ON THE ABOVELIST, HAVE BEEN FLAGGED AS CONTINUATION QUESTIONS:
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