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Physics 212 Lab Magnetic Fields and Forces Name 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 Identify patterns in the data and devise an explanation for an observed pattern Lab goals 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 Excel Introduction Magnetic fields measured in units of tesla T where 1 tesla 1 newton per amp meter 1 T 1 N A m They are produced by moving charges and hence also by electric currents The magnetic field produced by a current or moving charge can be determined by using two fundamental laws the Biot Savart law which is the magnetic analog of Coulomb s law for electricity and Amp re 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 moving B the force exerted on the charge by the in the presence of a magnetic field with velocity v field 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 the charged particle will always be perpendicular to both the velocity and the field We will make frequent 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 an electric current is simply the flow of charge So very similarly to Eq 1 we can write the force exerted 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 easuring the charge to mass M ratio electrons theory for In this first activity we will use the fact that magnetic fields exert a force on moving charges to determine the charge to mass e m ratio for electrons We will use a beam of electrons whose energy and hence speed can be controlled by varying a known accelerating voltage The electron beam is formed inside a glass sphere containing nitrogen at a residual pressure of approximately 10 2 torr When the electrons collide with the nitrogen molecules they cause the latter to emit a faint bluish radiation This glow will emanate from wherever the electrons collide with the gas molecules and as such will give us a visual cue visible in a darkened room as to what path the electrons are following The electrons will be emitted from an indirectly heated cathode and will be accelerated through a known electrostatic potential difference V after they are emitted By conservation of energy the potential energy lost by the electrons recall U q V as they move through the accelerating voltage V will be converted into kinetic energy Under the condition that the electrons accelerate from rest we can relate the kinetic energy gained to the potential energy lost via 1 2 m v2 eV or equivalently v 2 eV m 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 m v2 r Eq 6 evB e m v rB Using Eq 5 above we can eliminate the speed of the electrons in favor of the accelerating voltage V e m 1 rB 2 eV m m 1 e 2 2 V rB Eq 7 So if we simultaneously measure the radius r of the circular path the strength of the uniform magnetic field B and the accelerating voltage V then we will be able to determine the 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 coil separation d is set equal to the coil radius a The magnetic field along the axis has a uniform value B given by Eq 8 B 8 o 3 2 a 5 where N is the number of turns in each coil I is the current in each coil and a is again the radius of the coil For our apparatus N 130 and a 0 15 m With this information you can determine the magnetic field strength by measuring the electric current passing through the coils Lab Activity 1 Measuring the charge to mass ratio electrons 50 minutes for If you have not already done so carefully read the introduction of this activity to decide what quantities you will need to measure and how you will need to combine them in order to determine e m The apparatus to be used for this activity is shown below don t open the box for the actual experiment Helmholtz Coils Discharge Tube DC Power Supply Voltage Current Helmholtz Coil Current Control This equipment should have already been properly set up for you If it does not appear to be connected please make sure you consult your instructor Then follow the directions provided in precise order The equipment consists of two separate items as shown in the figure above The e m apparatus Helmholtz coil and discharge tube Note that the equipment as set up in the lab will have a wooden cover over this to make it easier to see the glowing electron path The discharge tube power supply Make sure that all the knobs on the power supply are turned all the way down counterclockwise and the Helmholtz coil current control indicated above is turned all the way up clockwise Switch the power supply on and wait for a couple of minutes for the cathode to heat up Start turning up the left voltage knob next to the blue dot on the power supply slowly

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