Physics Lab 212P-8
Moving Charges & Magnetic Fields
NAME:______
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LAB INSTRUCTOR:______
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Physics Lab 212P-8
Software List
Microsoft Excel
Equipment List (all items marked with * are in the student kit, others are supplied at the time of the lab)
*Two 1.5 V batteries + a battery holder
*Long (~2 ft) insulated wire
*Hookup wires with alligator clips
*Compass
Vertical stand with clamps
Experimental set-up for e/m ratio measurement
Physics Pre-lab 212P-8
Magnetic Fields and Electric Current
Name:______
Section:_____Date:______
(Read this & answer the questions before coming to lab)
Summary of relevant concepts:
- When an electric charge moves, it creates a magnetic field.
- Magnetic field is measured in units of "tesla" (T).
- Magnetic fields can exert a force on MOVING electric charges; for a charge q moving with a velocity v in a magnetic field B, this force F is given by:
- Since an electric current consists of moving charges, a magnetic field can also exert a force on a current; for a straight wire of length L and carrying a (conventional) current I, the force exerted by a magnetic field B is:
- The magnetic field created by a current can be calculated using two fundamental laws: the Biot-Savart Law and Ampere's Law;
- The Biot-Savart Law provides an expression for the magnetic field dB at a distance R from a differential element of wire dL carrying a current I:
Note that this is an inverse square law, similar to Coulomb's Law.
- Ampere's Law is useful in cases of obvious symmetry and relates the integral of the magnetic field B around a closed loop C to the TOTAL current I through the area bounded by the loop:
Pre-lab Questions:
A. Force exerted by a magnetic field on a moving charge:
Suppose an electron (charge e, mass m) is accelerated from rest through a potential difference V. It then enters a region of uniform magnetic field B, as shown in the figure below. The electron is moving in the plane of this page and the magnetic field is perpendicular out of the page. Answer the following questions based on this information. You will need these answers in the lab activity.
Q1. Determine an expression for the speed v of the electron just before it enters the magnetic field. (Hint: use energy conservation.)
Q2. Describe qualitatively why the electron moves in a circle once it enters the region of uniform magnetic field. Does the speed remain constant?
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Q3. Derive an equation for the charge-to-mass ratio e/m. The equation should contain the accelerating voltage V, the radius r of the electron's trajectory and the magnetic field B.
Q4. Using your result for Q3, what is the slope of the plot 1/r versus B equal to?
Q5. What approximately is the magnitude of the earth's magnetic field?
B. Magnetic Force on a Current
In the earlier exercise, you examined the force exerted by a magnetic field on a single electron. Although we do not readily "see" single electrons being affected by a magnetic field in everyday life, we do actually use this phenomenon in a very common technology: the electric motor! In an electric motor, a magnetic field exerts a force on a large number of electrons i.e. an electric current in a wire. You can qualitatively verify for yourself that the force on a current obeys the equation F = iL x B. Set up the experiment shown below but do NOT complete the circuit yet. Note that the insulated wire in your kit will obviously not allow you make the ideal shape shown in the figure. This is not really important: you just need a roughly straight horizontal portion of the wire above your magnet.
Q6. Use your compass to determine which end of your magnet is "North." Position your magnet with the N pole immediately below a roughly horizontal straight portion of your wire. Note down the direction in which current will flow when the circuit is completed. Watch the reaction of the reaction of the wire when you connect the battery for a few seconds. Repeat the experiment with (a) the current direction reversed and (b) with the S pole of the magnet pointing upwards. Describe and explain the reaction of the wire using F = iL x B.
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Lab Activity 1: A Magnetic Fields Exerts A Force On Moving Charges
(Measuring the Charge-to-Mass Ratio for Electrons)
The goal of this experiment is to study the motion of electrons in a uniform magnetic field and hence measure the charge-to-mass ratio for electrons. We use an electron beam 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. Collisions of the electrons with the nitrogen molecules cause the latter to emit a faint bluish radiation along the track of the beam that is visible in a darkened room. The electrons are emitted from an indirectly heated cathode, and are accelerated through a known electrostatic potential V after they are emitted. Then, the electron beam enters a region with a uniform magnetic field B. The essential physics is identical to the prelab (Q1-Q3). The uniform magnetic field is provided by a pair of current-carrying coils (known as a Helmholtz coil arrangement) with a coil separation d equal to the coil radius a. The magnetic field along the axis has a uniform value B given by (see -- for instance -- Halliday, Resnick & Walker, problem 30.64):
where N is the number of turns in each coil, I is the current in each coil and 0=4x107Wb/Am. For our apparatus, N= 130 and a = 0.15m. So, you can figure out the value of the magnetic field B by measuring the current I.
The equipment is shown in the figure on the next page. It should already have 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 experiment consists of two separate items as shown in the figure above:
- The e/m apparatus (Helmholtz coils & discharge tube -- left in figure); note that the equipment as set up in the lab will have a wooden cover over this;
- The discharge tube power supply (right in figure).
- 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 electrode to heat up.
- Start turning up the left voltage knob on the power supply slowly until you read a voltage of around 200V on the digital display. Note down the exact value of this voltage. Look through the window in the wooden cover at the right side of the glass sphere: you should be able to see an electron beam going vertically downwards.
- Now start turning up the current knob on the power supply till the current display reads about 2 A. The maximum current through the Helmholtz coils is 2 A, so please do not exceed this value. The electron beam should now be visible as a circle.
- Start varying the current using the Helmholtz coil current control on the e/m apparatus. Note that as you decrease the current, the diameter of the circle changes.
- You can see that the left side of the circle passes over numbers on a linear scale that glow as the beam hits them. The number that you read is the diameter of the circle in centimeters.
Q1. Record (in the table below) the current I through the Helmholtz coils and the diameter d of the circular electron path. Make sure that you convert the diameter into meters. Repeat this procedure for 10 different values of the current I.
I (A) / Diameter of Circle d (m)- Switch off everything: first turn the Helmholtz current control knob on the e/m apparatus all the way up; then turn down the current to zero using the knob on the power supply; after this, turn down the voltage to zero; finally, you can switch off the power supply.
- Enter the data from the table above into an Excel spreadsheet that:
- Converts your measured current I into a magnetic field B;
- Converts d into a column containing (1/r), where r is the radius of the circle (in meters).
Q2. Plot (1/r) vs. B using the linear fit from the WPTools menu on the Excel menu bar. Deduce an average value for the ratio e/m, including standard error, by fitting the data to a straight line. (Use your result from Q4 of the pre-lab and recall that the standard error is given by , where a1 is the slope of 1/r versus B.) Compare your measured value with the established one: 1.756 x 1011 C/kg. Include your Excel spreadsheet, graph and any relevant analysis with your report.
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Lab Activity 2: Moving Charges Create A Magnetic Field
(Magnetic Field Of A Current-carrying Wire)
Set up the experiment shown in the figure above using two 1.5 V batteries in series, the long insulated wire in your experimental kit and the stand/clamps provided in the lab. You can make contact to the wire by using a knife or blade to remove ~5 mm of insulation at each end. Make sure you don't use the bare Nichrome wires for this experiment. Note: do not keep the circuit fully connected except for short intervals when making observations -- otherwise you'll use up your batteries!
Q3. For the polarity of the batteries shown above, the conventional current in the wire travels vertically upwards. Use the Biot-Savart Law and/or a "right hand rule" to qualitatively sketch the magnetic field lines produced by this current.
Next, use your magnetic compass to confirm your expectations. Remember that the compass is always subject to the Earth's magnetic field, and is also affected by other external factors such as the proximity of other magnetic objects. Keep in mind that magnetic fields obey superposition, so that you can always subtract the effect of any "background" magnetic fields by carrying out measurements with and without a current in the wire. Finally, a cautionary note: the painted end of your compass needle is supposed to be the "North" pole of the needle; however, your compass needle may be mislabeled! Check to make sure which end of the needle is "North." Now that you have located "North", slowly move your compass around the wire while the circuit is not connected. Does the compass point consistently to the "North"? If not, you will need to move your test set up to a location where the stray magnetic fields are less noticeable.
Q4. While viewing your experimental set up from above, complete the following diagram to show the compass needle direction without and with current in the wire. One of the compass locations has been filled in for you.
Q5. By your observations in Q4, did the field produced by the current in the wire have a larger magnitude than the Earth's magnetic field? Do your results of Q4 confirm your expectations for the magnetic field produced by the current in the wire? Explain clearly why or why not?
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Q6. What do you expect will happen to the magnetic field lines if the current direction is reversed? Justify this using:
(a) the right hand rule
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(b) the Biot-Savart Law
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Describe the results of an experiment that tests your prediction.
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Q7. Order of magnitude estimate: what is the approximate magnetic field in the experiment you just carried out at a distance of 1 cm from the center of the wire? Specify your approximations and assumptions.
Compare this with the magnetic field of the Earth. Do your results agree with what you observed in Q4? Explain.
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Physics Post-lab 212P-8
Magnetic Fields and Electric Current
Name:______
Section:_____Date:______
The following graph is a plot of data from Physics 212P-8 Activity 1. 1/r versus B has been plotted. "Series 1 Fit" is a linear fit to the data and is of the form 1/r = a0 + a1 B, with SE(a0) and SE(a1) being the standard error for the intercept and slope respectively.
Q1. Given that and , where a1 is the slope of 1/r versus B. What is the value of e/m, including standard error, obtained from the above graph?
Q2. Does the value you obtain in Q4 agree with the generally accepted value of 1.756x1011 C/kg?
Yes No
Explain.