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# lab4 - Physics 7B Charge-to-mass e/m p 1 NAME GSI DL...

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Physics 7B Charge-to-mass: e/m p. 1 NAME: ______________________________ DL SECTION NUMBER: ___________________ GSI: _________________________________ LAB PARTNERS: _______________________ MAGNETISM LAB: The Charge-to-Mass Ratio of the Electron Introduction In this lab you will explore the motion of a charged particle in a uniform magnetic field, and determine the charge-to-mass ratio (e/m) of the electron. We hope that you will also begin to develop an intuitive feel for magnetism. There are more prelab exercises for this experiment than has been normal in Physics 7B. Be sure to complete these before arriving at lab—they will count for half of your final lab score, and your GSI will initial page 2 at the start of lab to indicate that you have completed them. We suggest reading through the entire lab before attempting to complete the Prelab questions, so that they will make more sense. Prelab Questions 1. Using your Physics 7B knowledge about the force on a charged particle moving in a magnetic field, and your Physics 7A knowledge of circular (centripetal) motion, derive an equation for the radius r of the circular path that the electrons follow in terms of the magnetic field B, the electrons’ velocity v , charge e, and mass m . You may assume that the electrons move at right angles to the magnetic field.

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Physics 7B Charge-to-mass: e/m p. 2 2. Recall from electrostatics, earlier in the course, that an electron obtains kinetic energy when accelerated across a potential difference V. Since we can directly measure the accelerating voltage V in this experiment, but not the electrons’ velocity v, replace velocity in your previous equation with an expression containing voltage. The electron starts at rest. (Don’t get capital V, voltage, confused with lowercase v, velocity.) Now solve this equation for e/m. You should obtain e m V B r = 2 2 2 Eq. 1
Physics 7B Charge-to-mass: e/m p. 3 3. The magnetic field on the axis of a circular current loop a distance z away is given by B IR R z = + ( ) μ 0 2 2 2 3 2 2 , Eq. 2 where R is the radius of the loop and I is the current. (See example in text for a derivation and discussion of this result.) Using this result, calculate the magnetic field at the midpoint along the axis between the centers of the two current loops that make up the Helmholtz coils, in terms of their number of turns N, current I, and radius R—see Fig. 2 on page 5. [Hint: magnetic fields add as any vector fields do.] Helmholtz coils are separated by a distance equal to their radius R. You should obtain B NI R NI R = = × 4 5 9 0 10 3 2 0 7 / . μ Eq. 2 where B is the magnetic field in tesla, I is the current in amps, N is the number of turns in each coil, and R is the radius of the coils in meters.

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