HW3-problems (1)

najjar (kgn294) – HW3 – li – (56955) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Consider the setup shown in the figure. Determine the force exerted by -Q on the dipole. Choose the correct expression for the force. + sign is along the positive x-direction. 1. + k q s Q z 2 2. + k q s Q z 3 3. − k q s Q z 2 4. − k 2 q s Q z 2 5. − k 2 q s Q z 3 6. + k 2 q s Q z 3 7. − k q s Q z 3 8. + k 2 q s Q z 2 002(part1of4)10.0points As you work with Coulomb’s law, you will often find you’d like to approximate expres- sions such as 1 ( r + s ) 2 for s ≪ r . Fortunately, there is an approximation method for this type of expression that is in- credibly common and is used throughout the sciences. We will call this method the small argumentapproximation , and its statement is: (1 + ǫ ) a ≈ 1 + aǫ for ǫ ≪ 1 , (1 + ǫ ) − a ≈ 1 − aǫ for ǫ ≪ 1 . Using this approximation method, 1 ( r + s ) 2 = ( r + s ) − 2 = 1 r 2 (1 + s/r ) − 2 ≈ 1 r 2 (1 − 2 s/r ) for s ≪ r , where s/r = ǫ satisfies the condition that ǫ ≪ 1. For each of the exercises below, assume x ≪ 1 and apply the small argument approxi- mation to determine the correct approximate expression. f ( x ) = 1 (1 + x ) 2 1. 1 + 2 x 2. 1 + x 2 3. 1 − x 2 4. 1 − 2 x 003(part2of4)10.0points f ( x ) = 1 1 + x 2 1. 1 + x 2. 1 − x 3. 1 − x 2 4. 1 + x 2 004(part3of4)10.0points f ( x ) = radicalBigg 1 1 + x 2

najjar (kgn294) – HW3 – li – (56955) 2 1. 1 − 1 2 x 2. 1 − 1 2 x 2 3. 1 + 1 2 x 2 4. 1 + 1 2 x 005(part4of4)10.0points One may approximate more complex expres- sions through successive application of the small argument approximation. Approximate the following expression by using the small argument approximation twice . f ( x ) = 1 parenleftBig 1 + 2 √ 1+ x parenrightBig 2 1. 1 9 parenleftbigg 1 + 1 3 x parenrightbigg 2. 1 9 parenleftbigg 1 − 1 3 x parenrightbigg 3. 1 9 parenleftbigg 1 − 2 3 x parenrightbigg 4. 1 9 parenleftbigg 1 + 2 3 x parenrightbigg 006(part1of3)10.0points A 1 . 28 µ C charge is at the origin and a − 5 . 34 µ C charge is 10 cm to the right, as shown. x O I II III y 1 . 28 µ C − 5 . 34 µ C 10 cm Identify the direction of vector E in the re- gion II (0 < x < 10 cm, along the x - axis). The value of the Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . 1. Up 2. Down 3. None of these 4. All possibilities: right, left, or zero 5. Right 6. Left 007(part2of3)10.0points Identify the direction of vector E in region III ( x > 10 cm along the x -axis). 1. Up 2. Right 3. All possibilities: right, left, or zero 4. Down 5. Left 6. None of these 008(part3of3)10.0points Determine the x -coordinate where vector E = 0. Answer in units of cm. 009 10.0points An electron and a neutral carbon atom of polarizability α are at a distance r apart ( r is much greater than the diameter d of the atom). Due to polarization of the atom by the electron, there is a force F between the electron and the carbon atom. If we change r to 2 r , what will be the ratio of F ′ F where F ′ is the new force between the two? Hint: To find the r -dependence of the force, first find the induced polarization (dipole moment) of the atom as a function of r . Then find the force exerted by this induced dipole on the electron. 010 10.0points Polarizability is defined by the relation vectorp = qvectors = α vector E ext , where α is polarizability and vector E ext is the external electric field that induces the polarization. We can obtain an estimate of

najjar (kgn294) – HW3 – li – (56955) 4 3. Diagram C 4. Diagram G 5. Diagram I 6. Diagram J 7. Diagram D 8. Diagram E 9. Diagram B 10. Diagram A 013(part3of8)10.0points Which of the following statements is correct? Enter all the apply, separated by commas. A. A molecule located at C would not be polarized at all. B. The polarization of a molecule located at D would be the same as the polarization of a molecule located at C . C. A molecule located at D would be po- larized more than a molecule located at C D. A molecule located at D would be po- larized less than a molecule located at C 014(part4of8)10.0points Which of the arrows (I-VIII) best indicates the direction of the electric field at location B due only to the dipole? 1. VI 2. VII 3. IV 4. V 5. I 6. III 7. VIII 8. II 015(part5of8)10.0points Which of the arrows (I-VIII) best indicates the direction of the electric field at location B due only to the plastic block? The magnitude o the electric field at B due to the plastic is less than the magnitude of the electric field at B due to the dipole. 1. IV 2. V 3. II 4. I 5. III 6. VII 7. VIII 8. VI 016(part6of8)10.0points Which of the arrows (I-VIII) best indicates the direction of the net electric field at loca- tion B ? 1. V 2. II 3. III 4. I 5. IV 6. VI 7. VIII 8. VII

najjar (kgn294) – HW3 – li – (56955) 5 017(part7of8)10.0points Which of the following statements is correct? Enter all that apply, separated by commas. A. The net electric field at B would be larger if the plastic block were not there. B. The net electric field at B would be the same if the plastic block were not there. C. The net electric field at B would be smaller if the plastic block were not there. D. The net electric field at B would be zero if the plastic block were not there. 018(part8of8)10.0points Using the diagrammatic conventions dis- cussed in the text, a student drew the dia- gram in the following figure to help answer the questions asked above. Which of the follow- ing statements about the student’s diagram are true? Enter all that apply, separated by commas. C D + − Plastic block − − − − − − − − − − − + + + + + + + + + + + A. The direction of polarization of the plas- tic block is wrong. B. The diagram is correct; this is just a different way of drawing the polarization. C. The diagram shows mobile charges; this is wrong because an insulator does not have mobile charged particles. 019 10.0points A very thin spherical plastic shell of radius R = 18 cm carries a uniformly distributed negative charge of Q = − 5 nC on its outer surface. An uncharged solid metal block is placed nearby. The block is w = 11 cm thick and is 11 cm away from the surface of the sphere. Calculate the magnitude of the elec- tric field at the exact center of the conductor generated only by the polarization of the con- ductor. In other words, do not include the electric field generated by the sphere. Answer in units of N / C.