University of Texas

PHYSICS 303

This print-out should have 34 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points 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 2.2r, 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. Correct answer: 0.019404. Explanation: The force will be proportional to r −5 and hence the correct answer will be F ′ F = 0.019404 . 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 Ee = 1 4πǫ0 e r 2 From this, the magnitude of the induced dipole moment of the carbon atom can be written down as p = αEe. This dipole moment 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 Ep = 1 4πǫ0 2p 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 = Ep e. Combining all the equations, we get F = Ep e = 1 4πǫ0 2αEe e r 3 =  1 4πǫ0 2 2αe2 r 5 This implies that when r to 2.2r, the electric field field, and consequently the force, is decreased by a factor of (2.2)−5 = 0.019404, and hence the answer is F ′ F = (2.2)−5 = 0.019404 002 (part 1 of 4) 10.0 points A charged particle with charge q1 is a distance r from a neutral atom, as shown in the following figure. q1 Charge Neutral atom r If q1 is negative, which diagram (A-J) in the following figure best shows the charge distribution in the neutral atom in this situation? A B C D E F G H I J − + + − − + − + − + − + − + − + Other Correct answer: B. Explanation: If q1 is negative, then the field at the location of the neutral atom will point toward the left. In that case, the positively charged nucleus, like always, follows the field and moves toward the left, while the negatively charged electron cloud will move opposite to the field and shift toward the right. 003 (part 2 of 4) 10.0 points Which of the arrows in the following diagram best indicates the direction of the electric field lui (el22284) – HW3 – li – (58545) 2 at the location of the charged particle, made by the polarized neutral atom? A B C D E F G H Correct answer: G. Explanation: The dipole moment of the neutral atom points to the left, and the electric field due to the induced dipole at points along the axis of the dipole is in the same direction as the dipole moment. 004 (part 3 of 4) 10.0 points Which of the arrows in the diagram from part 2 best indicates the direction of the force on the negatively charged particle, due to the polarized neutral atom? Correct answer: C. Explanation: The force on a negatively charged particle is opposite the electric field at its location. Also, remember that induced dipoles never repel their inducing charge. 005 (part 4 of 4) 10.0 points Which of the arrows in the diagram from part 2 best indicates the direction of the force on the polarized neutral atom, due to the charged particle? Correct answer: G. Explanation: There are multiple explanations including: (1) Newton’s second law says that interacting objects will exert equal magnitude forces on each other, in opposite directions; (2) superposition of forces on the “side” of the dipole results in a net force in the direction of the force on the side of the dipole that is nearest the charged particle. 006 10.0 points A large positive charge pulls on a distant electron. How does the net force on the electron change if a slab of neutral glass is inserted midway between the large positive charge and the electron? Enter the letter corresponding to the correct choice. A. The net force is unchanged because the positive charge has no effect on the neutral glass and the E-field of the positive charge is unaffected by the glass. B. The net force increases because the glass is polarized by the positive charge and generates a small additional E-field in the same direction as the field of the positive charge. C. The net force decreases because the glass reduces the strength of the electric field that passes through it. D. The net force decreases because the glass is polarized by the positive charge and generates a small additional E-field in the opposite direction as the field of the positive charge. Correct answer: B. Explanation: The first statement is false. The molecules in the glass are polarized by the field of the positive charge. The second statement is true. The glass is polarized, and the molecules in the glass acquire a dipole moment aligned with the Efield of the positive charge. As a consequence, the glass generates a (small) E-field at the location of the electron in the same direction as the field of the inducing positive charge. Statement C is false. The electric field of the positive charge is unaffected by the glass (superposition principle). Statement D is false. The glass is polarized, but in the opposite direction. 007 10.0 points Polarizability is defined by the relation ~p =