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new-final-chiu-solutions

new-final-chiu-solutions - Version 005 new-final-chiu...

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Version 005 – new-final-chiu – chiu – (56565) 1 This print-out should have 25 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 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 3 r , what will be the new force F 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. 1. F = F 243 correct 2. F = 27 3. F = F 4. F = F 3 5. F = F 81 6. F = F 9 7. F = 9 F 8. F = 3 F 9. F = F 27 Explanation: The force will be proportional to r 5 and hence the correct answer will be F = F 243 . The calculation is as follows. The magnitude of electric field due to the electron at the location of the carbon atom will be given by E e = 1 4 πǫ 0 e r 2 From this, the magnitude of the induced dipole moment of the carbon atom can be written down as p = αE e . This dipole mo- ment will be pointing towards the electron, and hence the electron will lie on the axis of this dipole. The magnitude of the electric field due to this dipole at the location of the electron will be given by E p = 1 4 πǫ 0 2 p r 3 Here, we have used the fact that r >> d . The magnitude of force on the electron due to the dipole (and vice versa) can be obtained as F = E p e . Combining all the equations, we get F = E p e = 1 4 πǫ 0 2 αE e e r 3 = parenleftbigg 1 4 πǫ 0 parenrightbigg 2 2 αe 2 r 5 This implies that when r to 3 r , the electric field field, and consequently the force, is de- creased by a factor of 3 5 = 243, and hence the answer is F = F 243 . 002 10.0points An electron oscillating along the y -axis with angular frequency ω and amplitude A passes through the origin at time t = 0 and is moving in the + y direction. Which formula desribes the time dependence of E rad at a point vectorp = ( x, x/ 3 , 0 ) ? (Note: ˆ n is the unit vector along the direc- tion of vectora an instant after t = 0.) 1. 3 8 πǫ 0 2 A c 2 x sin( ωt n 2. 1 4 πǫ 0 2 A c 2 x sin( ωt n 3. 3 8 πǫ 0 2 A c 2 x sin( ωt n 4. 3 16 πǫ 0 2 A c 2 x sin( ωt n 5. 3 16 πǫ 0 2 A c 2 x sin( ωt n 6. 3 16 πǫ 0 2 A c 2 x sin( ωt n

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Version 005 – new-final-chiu – chiu – (56565) 2 7. 1 4 πǫ 0 2 A c 2 x sin( ωt n 8. 3 16 πǫ 0 2 A c 2 x sin( ωt n correct Explanation: First we note that the point vectorp makes a 30 angle with the xz plane. Calling the angle between vectorp and the xz plane θ , we can see this from tan θ = parenleftbigg x 3 parenrightbigg x = 1 3 and the fact that tan(30 ) = 1 / 3.
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new-final-chiu-solutions - Version 005 new-final-chiu...

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