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# Central Penn College PHY 212 - Lab: Magnetic Fields and Forces

Course: Phy 212-
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Physics Goals:Equipment:Introduction:Lab Activity 1: Measuring the charge-to-mass ratio for electrons (theory)Lab Activity 1: Measuring the charge-to-mass ratio for electrons (50 minutes)Lab Activity 2: Examining the magnetic field of a current-carrying wire (50 minutes)Physics 212 Lab: Magnetic Fields and ForcesName: Nirmit Rathod Name: Nicolas Leone Name: Date: 04/06/2022 Lab Sect.: Physics Goals:- To examine the effect that magnetic fields have on moving charges.- To examine the magnetic field produced by a long, straight current-carrying wire.Lab goals:- Identify patterns in the data and devise an explanation for an observed pattern.- Use spreadsheets to create scatter plot to visualize data.- Generate “best fit” slope and intercept to find the values of physical quantities.- Incorporate correct physical terminology into discussion of experimental data and argument of experimental results.- Identify the claims, theoretical background, experimental evidence, and logical connections that hold their own written arguments together.Equipment:- Phys212 LabKit Module- Magnetic compass- (2) Stackable banana-plug connecting wires- 2-m length of insulated wire- Vertical stand, clamp, and horizontal rod- e/m equipment (Helmholtz coil, discharge tube, power supply)- Software: Microsoft ExcelIntroduction:Magnetic fields measured in units of tesla (T), where 1 tesla = 1 newton per amp-meter (1 T = 1N / A·m). They are produced by moving charges (and hence, also by electric currents.). Themagnetic field produced by a current or moving charge can be determined by using twofundamental laws: the Biot-Savart law (which is the magnetic analog of Coulomb’s law forelectricity) and Ampère’s law (which is the magnetic analog of Gauss’ law for electricity). Complimentarily, magnetic fields can also exert a force on moving charges. For a charge q movingwith velocity vin the presence of a magnetic field B the force exerted on the charge by thefield is given by F=qv ×B (Eq. 1)Note the cross product in the above calculation: this implies that the direction of the force on thecharged particle will always be perpendicular to both the velocity and the field. We will makefrequent use of the right-hand rule to help us determine the direction of this force.A magnetic field will also exert a force on a current-carrying wire. This should make sense, as anelectric current is simply the flow of charge. So, very similarly to Eq. 1, we can write the forceexerted by a magnetic field Bon a straight wire of length L carrying a current i asF=iL ×B, (Eq. 2)where the direction of L is defined to be the direction of the (conventional) current.Lab Activity 1: M easuring the charge-to-mass ratio for electrons (theory) In this first activity, we will use the fact that magnetic fields exert a force on moving charges todetermine the charge-to-mass (e/m) ratio for electrons. We will use a beam of electrons whoseenergy (and hence speed) can be controlled by varying a known accelerating voltage. Theelectron beam is formed inside a glass sphere containing nitrogen at a residual pressure ofapproximately 10−2 torr. When the electrons collide with the nitrogen molecules, they cause thelatter to emit a faint bluish radiation. This glow will emanate from wherever the electrons collidewith the gas molecules, and as such, will give us a visual cue (visible in a darkened room) as towhat path the electrons are following.The electrons will be emitted from an indirectly heated cathode, and will be accelerated through aknown electrostatic potential difference V after they are emitted. By conservation of energy, thepotential energy lost by the electrons (recall: ΔU = qΔV) as they move through the acceleratingvoltage V will be converted into kinetic energy. Under the condition that the electrons acceleratefrom rest, we can relate the kinetic energy gained to the potential energy lost via12m v2=eVor, equivalently,v=√2 eVm(Eq. 5)After the electrons have been accelerated up to this speed v, the electron beam enters a region with a uniform magnetic field B, with the field oriented perpendicular to the motion of the beam. Upon entering this region, the electrons in the beam will travel a circular path at the constant speed v. Recall that, for any massive object to travel in a circular path at a constant velocity, a force must be continuously directed toward the center of the circle. Here, the magnetic force on the moving charge is providing this centripetal force. We thus set the force on a charged particle in a magnetic field (Eq. 1) equal to the centripetal force, and solve for the ratio e/m:evB=m v2r em=v❑rB (Eq. 6)Using Eq. 5 above, we can eliminate the speed of the electrons in favor of the accelerating voltage V: em=1rB√2 eVm (em)12=√2 VrB (Eq. 7)So, if we simultaneously measure the radius r of the circular path, the strength of theuniform magnetic field B, and the accelerating voltage V, then we will be able to determinethe ratio e/m for an electron.To create the uniform magnetic field in this experiment, we will use a pair of current-carrying coils (known as a Helmholtz coil arrangement). In this configuration, the coilseparation d is set equal to the coil radius a. The magnetic field along the axis has auniform value B given by B=8 μo∋¿532a¿ (Eq. 8)where N is the number of turns in each coil, I is the current in each coil, and a is again, theradius of the coil. For our apparatus, N= 130 and a = 0.15 m. With this information, you candetermine the magnetic field strength by measuring the electric current passing through thecoils.Lab Activity 1: Measuring the charge-to-mass ratio for electrons (50 minutes) If you have not already done so, carefully read the introduction of this activity to decidewhat quantities you will need to measure and how you will need

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