1 of 12 Q21-1. Two uniformly charge spheres are attached to frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces on the two spheres? Answer: D (By Newton's 3rd Law and by the form of Coulomb's Law) Q21-2. Two protons are near each other. Each feels an electrostatic repulsion of magnitude Felec and a gravitational attraction of magnitude Fgrav, due to the other charge. As the charges are moved apart, the ratio elecgravFF… A) increases B) decreases C) remains constant Answer: remains constant A) E) D)B)C) 9/10/2009 PHYS1120 Dubson Fa09 ©University of Colorado2 of 12 Q21-3. An electric dipole consists of two equal and opposite charges (+Q and –Q) separated by some fixed distance d . A charge +q is brought near the dipole and is positioned so that the distances to the +Q and the –Q charges are identical as shown below: What is the direction of the net electrostatic force on the +q charge? Answer: to the right (Be sure you can draw the vector diagram, showing the forces on +q) Q21-4. What is the correct expression for the y-component of the force on +q due to the other charges +Q and –Q ? A) 2Qqkr+ B) 2Qqkr− C) 2Qq2kr+ D) 2Qqk2r− E) None of these! Answer: 2Qqkr− (Notice that the y-component of the force is negative) +Q d –Q +q D C B A E) Some other direction +Q r –Q +q y r x 9/10/2009 PHYS1120 Dubson Fa09 ©University of Colorado3 of 12 Q21-5. Vector Review: How many of these equation make no sense? • ˆAj=JG• ˆˆ ˆB3ij5j=+−JG • AC3=KJG • ˆCAi=+JG J G• ˆC4i=−JG A) 0 (All make sense) B) 1 C) 2 D) 3 E) 4 Answer: The last one makes no sense. You can't add a number and a vector. All the others makes sense. ˆC4i=−JG Q21-6. Trig Review: In a tilted xy coordinate system, the weight vector mg is straight down. The coordinates are tilted at an angle θ as shown. What is Wy , the y-component of the weight mg? A) +mg sinθ B) –mg cosθ y C) –mg sinθ D) +mg E) 0 θ mg x Answer: –mg cosθ (careful with the signs!) 9/10/2009 PHYS1120 Dubson Fa09 ©University of Colorado4 of 12 Q21-7. An electric dipole (+Q and –Q separated by a distance d ) is placed along the x-axis as shown. A positive test charge +q is placed at position A to the right of the dipole. +Q +q The positive test charge feels a force that is A) zero. B) to the right. C) to the left. If the test charge +q is removed, electric field at position A is A) zero. B) to the right C) to the left D) There is no electric field at point A, when the test charge is removed. If a negative test charge –q is used to measure the Electric field at A, the electric field at position A is A) zero. B) to the right C) to the left Answers: The force on +q is to the left. The E-field at A points to the left, regardless of whether the test charge is positive (+q) or negative (–q). Q21-8. Two charges +Q and – Q are located on the x-axis as shown, what is the magnitude of the electric field at point A? A) kQR2119⋅−⎛⎝⎜⎞⎠⎟ B) ⎟⎠⎞⎜⎝⎛−⋅4112RkQ C) Zero D) kQR2191⋅−⎛⎝⎜⎞⎠⎟ E) None of these. Answer: kQR2119⋅−⎛⎝⎜⎞⎠⎟ x+Q–Q RR R AA –Q x 9/10/2009 PHYS1120 Dubson Fa09 ©University of Colorado5 of 12 Q21-9. Two positive charges, each of size +Q, are equal distances from the origin as shown. What is the direction of the electric field at the point in empty space which forms a square with the two charges and the origin? Answer: B (upper right) Q21-10. Two vectors A are shown. Consider the vector sum and BJG JGCAB=+JGJGJG. What is Cy, the y-component of ? CJG A: 3 B: 2 C: –2 D: –4 E: None of these/don't know. Answer: Cy = Ay + By = +1 – 3 = –2 +Q y A B Field here? +Q D C x E) No Field there B A x y 9/10/2009 PHYS1120 Dubson Fa09 ©University of Colorado6 of 12 Q21-11. A point in empty space is near 3 charges as shown. The distances from the point to each of the three charges are identical. The direction of the electric field at that point is.. A: Some angle less than 45o below the +x-direction. B: 45o below the +x-direction. C: along the +y directions D: Some other angle. E: The electric field at that point is zero. Answer: 45o below the +x-direction. (Be sure you can draw the E-field diagram.) +Q +Q C A +2Q B 9/10/2009 PHYS1120 Dubson Fa09 ©University of Colorado7 of 12 Q21-12. Three charges of equal magnitude are arranged as shown. What is the direction of the electric field at point x? An electron is fired into the region of the three charges from the lower right as shown. What is the direction of the acceleration of the electron when it is at point x? Answers: The direction of the E-field at point x is straight up (choice A). The direction of the acceleration of an election is the direction of a = F/m = qE/m = –eE/m (vector quantities are in bold here), which is the direction opposite of the E-field. So the direction of the acceleration is straight down (None of these). A D C B E) None of these. x D E) None of these. A B C x 9/10/2009 PHYS1120 Dubson Fa09 ©University of Colorado8 of 12 Ch26-13. A charge Q is on the y-axis at y = d. What is the magnitude of the E-field at position x, on the x-axis? A) ()2kQdx+ y Q B) 22kQxd+ C) ()222kQxd+ d D) 22kQxd+ θ xE E) None of these What is Ex the x-component of E at position x on the x-axis? A) 22dExd+ B) 22xExd+ C) 222xExd+ D) None of these Answers: E = 2kQxd+2, Ex = +E cosθ = 22xExd+ Ch26-14. What is the magnitude of the electric field at point x on the x-axis due to the two +Q charges shown on the y-axis? y +QA) ()3/2222kQxxd+ d E = ? B) ()1/2222kQdxd+ x d C) ()1/2222kQxxd+ D) None of these +Q Answer: ()3/2222kQxxd+ (see the previous problem to see why)9/10/2009 PHYS1120 Dubson Fa09 ©University of Colorado9 of 12 Q21-15. Two socks are observed to attract each other. Which, if any, of the first 3 statements MUST be true? (emphasis on MUST) A) The socks both have a non-zero net charge of the same sign. B) The socks both have a charge, of opposite signs. C) Only one sock is charged; the other is neutral. D) None of the preceding statements must be true. Answer: D. The socks might be attracting because they have opposite sign
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