PHY 59130 .OHW 20[explained solutions LATEST 2020]GRADED A+

Document Content and Description Below

This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points A device (“source ... ”) emits a bunch of charged ions (particles) with a range of velocities (see figure). Some of these ions pass through the left slit and enter “Region I” in which there is a vertical uniform electric field (in the −ˆ direction) and a 0.1 T uniform magnetic field (aligned with the ±ˆk-direction) as shown in the figure by the shaded area. q m Region of Magnetic Field 0.1 T +1000 V 1.2 cm x y z 28 cm Region I Region II Figure: ˆı is in the direction +x (to the right), ˆ is in the direction +y (up the page), and ˆk is in the direction +z (out of the page). In which direction (relative to the coordinate system shown above) should the magnetic field point in order for negatively charged ions to move along the path shown by the dotted line in the diagram above? 1. kB~ k = 0 ; direction undetermined 2. B~ kB~ k = +ˆk 3. B~ kB~ k = −ˆk correct Explanation: To obtain a straight orbit, the upward and downward forces need to cancel. The force on a charged particle is F~ = F~E + F~B = q (E~ +~v × B~ ). For the force to be zero, we need F~E + F~B = 0 , or F~E = −F~B . Therefore, the forces are equal and opposite and the magnitude of forces are equal; i.e., kF~Ek = kF~Bk . The force due to the magnetic field provides the centripetal force that causes the positive ions to move in the semicircle. As the negatively charged ion exits the region of the electric field, F~ B = q ~v × B~ , so by the right-hand rule the magnetic field must point out of the page  or in the −z-direction −ˆk  , since the force F~ is in the direction down the page; i.e., “−ˆ ” q |q| = − ~v k~vk = +ˆı B~ kB~ k = ? F~ B kF~ B k = −ˆ , and the vector product ˆı × ˆk = −ˆ , and since F~ = q ~v × B~ = kF~ k (−ˆ) F~ kF~ k = q |q| " ~v k~vk × B~ kB~ k # = − h (+ˆı) ×  −ˆk i = −ˆ , consequently B~ kB~ k = −ˆk is correct. 002 (part 2 of 3) 10.0 points In “Region I”, the electric potential between the plates is 1000 V, the distance between the plates is 1.2 cm, and the magnetic field in both “Regions I and II” is 0.1 T . This study source was downloaded by 100000825292796 from CourseHero.com on 05-04-2021 18:42:55 GMT -05:00 https://www.coursehero.com/file/5790232/OHW-20/ This study resource was shared via CourseHero.com terry (ect328) – oldhomework 20 – Turner – (59130) 2 What is the speed of a singly charged ion that passes through both slits and makes it into “Region II”? Correct answer: 8.33333 × 105 m/s. Explanation: Let : B = 0.1 T , and E ≡ V d = (1000 V) (1.2 cm) = 83333.3 N/C . Since the electric and magnetic forces on the ion are equal, q E = q v B v = E B = 83333.3 N/C 0.1 T = 8.33333 × 105 m/s . 003 (part 3 of 3) 10.0 points The ions that make it into “Region II” are observed to be deflected downward and then follow a circular path with a radius of r = 0.28 m. The charge on each ion is 1.5 × 10−18 C. What is the mass of the ions? Correct answer: 5.04 × 10−26 kg. Explanation: Let : r = 0.28 m = 0.28 m and q = 1.5 × 10−18 C . The radius of a circular path taken by a charged particle in a magnetic field is given by r = m v q B . m = q B r v = (1.5 × 10−18 C) × (0.1 T)(0.28 m) 8.33333 × 105 m/s = 5.04 × 10−26 kg . 004 (part 1 of 6) 10.0 points A particle of mass 4.316 × 10−26 kg and charge of magnitude 3.2 × 10−19 C is accelerated from rest in the plane of the page through a potential difference of 409 V between two parallel plates as shown. The particle is injected through a hole in the right-hand plate into a region of space containing a uniform magnetic field of magnitude 0.217 T oriented perpendicular to the plane of the page. The particle curves in a semicircular path and strikes a detector. q m Region of Magnetic Field B E hole What is the sign of the charge of the particle? Neglect relativistic effects. 1. The charge q cannot be determined for information given. 2. The charge q is negative, − . 3. The charge q is positive, + . correct Explanation: The charge accelerates toward the negative plate and away from the positive plate. Therefore the charge is positive, + . 005 (part 2 of 6) 10.0 points Which way does the magnetic field point? 1. out of the page correct 2. to the left 3. into the page 4. toward the top of page 5. toward the bottom of page [Show More]

Last updated: 3 years ago

Preview 1 out of 4 pages