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Ch14-h3-solutions

# Ch14-h3-solutions - liu(ql744 Ch14-h3 chiu(56565 This...

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This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Which of these statements about a dipole are correct? 1 The electric field at any location in space, due to a dipole, is the vector sum of the electric field due to the positive charge and the electric field due to the negative charge 2 The net electric field due to a dipole is zero, since the contribution of the negative charge cancels out the contribution of the positive charge 3 At a distance d from a dipole, where d s (where s is the separation of the charges), the magnitude of the electric field due to the dipole is proportional to 1 d 3 4 When placed in a constant electric field, a dipole does not interact at all, since the force on the positive charge is in an opposite direction to the force on the negative charge 5 Dipoles can be detected by having an ex- ternal field cause them to vibrate Your answer should be a list of numbers corresponding to the correct statements, with the numbers separated by commas Correct answer: 1,3,5. Explanation: Let’s examine each of these claims individ- ually: 1 Any electric field is the vector sum of the individual charges that cause the electric field to be formed. This is known as the principle of superposition. 2 Although the charges in a dipole have equal magnitude, they are in di ff erent locations For this reason, a typical point will be a di ff erent distance away from each of the two dipole charges, and the vector sum of the two fields will be nonzero. 3 We can derive this relationship using Coulomb’s law. Let the charge on the dipole be q , and their separation distance be a . For simplicity, consider a point on the line connecting the two charges, a distance x from the positive charge. Then, the net field lies on the x -axis, and has magnitude: E = k q r 2 - k q ( r + a ) 2 = kq ( r + a ) 2 - r 2 ( r ( r + a )) 2 = kq r 2 + 2 ra + a 2 - r 2 ( r ( r + a )) 2 = kq 2 ra + a 2 ( r ( r + a )) 2 So, when r is much larger than a , we have E kq r 3 . 4 While the forces on the charges on a dipole are equal in magnitude and in opposite di- rections, they are applied in di ff erent loca- tions, which will create a net torque on the dipole, even if the net force is zero. 5 This is in fact a common technique for de- tecting dipoles. Since a net torque is cre- ated on a dipole in a uniform field, and this torque depends sinsuoidally on the angle between the field and the dipole moment, the dipole will oscillate according to the same equations as you would use for a pen- dulum. 002 (part 1 of 2) 10.0 points A charge of 1 nC (1 nC = 1 × 10 - 9 C) and a dipole with charges + q and - q separated by 0 . 3 mm contribute to a net field at location A that is zero, as shown in the following figure.

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A 12 cm 20 cm + +1 nC Which end of the dipole is positively charged?
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Ch14-h3-solutions - liu(ql744 Ch14-h3 chiu(56565 This...

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