1 of 13Q21-1 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 constantAnswer: remains constant1/14/2019 PHYS1120 Dubson Fa09 ©University of ColoradoA)E)D)B)C)+ +2 of 13Q21-3 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) 2Q qkr+B) 2Q qkr-C) 2Q q2 kr+D) 2Q qk 2r-E) None of these!Answer: 2Q qkr- (Notice that the y-component of the force is negative)1/14/2019 PHYS1120 Dubson Fa09 ©University of Colorado+Qd–Q+qDCBE) Some other directionA+Qr–Q+qrxy3 of 13Q21-5 Vector Review: How many of these equation make no sense?-�A jur-� � �B 3i j 5j ur-AC3=vur-�C A i ur ur-ˆC 4 i= -ur A) 0 (All make sense) B) 1 C) 2 D) 3 E) 4Answer: The last one ˆC 4 i= -ur makes no sense. You can't add a number and a vector. All the others makes sense.Q21-6 Trig Review: In a tilted xy coordinate system, the weight vector mg is straight down. The coordinates are tilted at an angle - as shown. What is Wy , the y-component of the weight mg?A) +mg sin- B) –mg cos- C) –mg sin- D) +mg E) 0Answer: –mg cos- (careful with the signs!)1/14/2019 PHYS1120 Dubson Fa09 ©University of Coloradoyx-mg4 of 13Q21-7 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. 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 theelectric field at point A?A) kQR2119 B) 4112RkQC) Zero D) kQR2191 E) None of these.Answer: kQR2119 1/14/2019 PHYS1120 Dubson Fa09 ©University of Colorado+qAx+Q–Qx+Q–QRRRA5 of 13Q21-9 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 and Bur ur are shown. Consider the vector sum C A B ur ur ur. What is Cy, the y-component of Cur?A: 3B: 2C: –2D: –4E: None of these/don't know.Answer: Cy = Ay + By = +1 – 3 = –21/14/2019 PHYS1120 Dubson Fa09 ©University of Colorado+Q+QDCABFieldhere?xyE) No Field thereB A x y6 of 13Q21-11 A point in empty space is near 3 charges as shown. The distances from the point to eachof 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 directionsD: 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.)1/14/2019 PHYS1120 Dubson Fa09 ©University of Coloradoxy+Q+Q+2QABC7 of 13Q21-12 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).1/14/2019 PHYS1120 Dubson Fa09 ©University of ColoradoADCBE) None of these.xADCBE) None of these.xxABC8 of 13Ch26-13 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) ( )2kQd x+B) 2 2kQx d+C) ( )22 2kQx d+D) 2 2kQx d+E) None of theseWhat is Ex the x-component of E at position x on the x-axis?A) 2 2dEx d+B) 2 2xEx d+C) 22 2xEx d+D) None of theseAnswers: E = 2 2kQx d+, Ex = +E cos- = 2 2xEx d+Ch26-14 What is the magnitude of the electric fieldat point x on the x-axis due to the two +Q chargesshown on the y-axis?A) ( )3/ 22 22 k Q xx d+B) ( )1/ 22 22 k Q dx d+C) ( )1/ 22 22 k Q xx d+D) None of theseAnswer: ( )3/ 22 22 k Q xx d+ (see the previous problem to see why)1/14/2019 PHYS1120 Dubson Fa09 ©University of ColoradoyQxdE-y+Qxdd+QE = ?9 of 13Q21-15 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 charges. Or it could be that only one of them is charged and the other is neutral, in which case the attraction is due to polarization of the neutral sock.Q21-16 A dipole is placed in an external field as shown. In which situation(s)
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