Electric potentials and and EKG measurements

In this laboratory you will explore the connection between electric field lines and equipotential surfaces, and you will use a PASCO EKG sensor to measure the action potential of your heart.  Objects with net electric charge attract or repel each other.  If you want to change the position of a charged object relative other charged objects, you, in general, have to do (positive or negative) work.  But sometimes it is possible to move a charged object relative to other charged objects along a surface without doing any work.  The potential energy of the charged object does not change as you move it.  If an electric charge can travel along a surface without the electric field doing any positive or negative work, then the surface is called an equipotential surface.

Equipment needed:

• EKG sensor
• Electrode patches
• Rubbing alcohol

Open a Microsoft Word document to keep a live journal of your experimental procedures and your results.  Include all deliverables, (data, graphs, analysis, outcome).  Write a 'mini-reflection' immediately after finishing each investigation, experiment or activity, while the logic is fresh in your mind.

Experiment: 

The main electrical pulse of the heart (the QRS complex) creates a net electric dipole pointing down and to the person's left.  Sketch the electric field lines and equipotential curves across a human torso for this dipole.  Based on your sketch, if you place a positive voltage lead on the left arm and a negative lead on the right arm, should the measured potential difference ∆V = V_left - V_right be positive or negative during the peak pulse?  What if you swapped the leads?

You will use the PASCO EKG sensor to measure the action potential of your heart.
What does the EKG measure?
Caution:  The sensor used in this laboratory will give you a good view of the electrical activity of the heart, but it is not an instrument to be used for medical diagnosis.  The interpretation of electrocardiograms for diagnosis requires significant training and experience, something that many of you can look forward to acquiring in the near future.

Collecting your data

Pick one person to be the subject in your group.  If you have time, you can repeat the experiment with another person as the subject. 
Use the following guidelines to make the EKG measurement.

Obtain a paper towel and a little rubbing alcohol.  With the dampened paper towel wipe off an area inside each elbow and inside of the right wrist.

Obtain three electrode patches from your instructor.  The patches have been designed to reduce the resistance of your skin.

Firmly place the electrode patches onto your skin - one on your right wrist, one on the inside of the right elbow, and one on the inside left elbow (as pictured).  Leave them in place until you have completed all EKG activities.
Caution:  A very small fraction of students may be allergic to the electrodes.  If you feel a burning sensation or are extremely uncomfortable, then remove the electrodes immediately and rinse the area.

Make sure the Pasco 850 interface is turned on.  Open the Capstone program.  The icon for this program is on the desktop.

• We have two versions of EKG sensors.  If your sensor is a CI-6539A sensor with a black DIN cable, then connect the EKG sensor to analog channel A of the Pasco 850 interface box.  In the Capstone program, click the Hardware Setup button, double click Analog Channel A and choose to add the EKG sensor.  Click Hardware Setup again to close this window.
• If your sensor is a Passport sensor with a silver cable, then plug the EKG sensor into Passport 1 of the Pasco 850 interface box.  It will be automatically recognized.  You can verify this by clicking the Hardware Setup button.

Drag a Graph icon onto the main display.  For the vertical axis choose Amplitude (mV).  Set the sample rate to 250 Hz.

Connect the EKG sensor to the electrodes.  The reference (black) lead should be connected to your wrist.  This lead will be the "flat line" potential on your EKG.  The positive (red) lead should be connected to the electrode on your left elbow.  Finally the negative (green) lead should be connected to the electrode on your right elbow.  Try to adjust the wires so that they are not twisting or pulling on the electrodes.

Once you are safely and securely connected to the EKG sensor, remain fairly still and breathe normally.  A lab partner should operate the computer and start collecting the data.

Start collecting data.  Collect enough data for about 5-10 heartbeats.
Save the file with your data for further analysis and paste the graph into your journal.

Disconnect the EKG sensor from the electrodes, but leave the electrodes attached to your arms.

Analyzing your data

Using your data, determine the following for your heart. 

(a) Peak-to-peak value of the voltage between the R wave and the S wave.
(b) The P-R time interval.
(c) The Q-R-S time interval.
(d) The Q-T time interval.
(e) The frequency of your heart during data collection (in beats/min and in Hz)?

Guess what would happen if you switched the red and green leads?  Try it out experimentally and make a sketch of your results in your journal.  Explain any differences that may occur due to this change.

Collecting more data

EKG after mild exercise:  When your heart rate doubles during exercise, the time between beats (the R - R interval) drops by half.  Do all parts of the waveform shrink equally (P wave, QRS complex, T wave, and T-P rest interval), or does one specific interval account for most of the time change?  Draw your predicted post-exercise trace over your resting trace.
 

Have your subject stand up and exercise for three minutes (jog in place, "step in time", walk up and down the stair case, walk briskly around the hallway, ...).   After the three minutes are up, have the person sit back down and get reconnected to the EKG sensor as quickly as possible.  Collect a new set of data.  Save the file with the data for further analysis and paste the graph into your log. 

Using your data, determine the following for your heart.

(a) Peak-to-peak value of the voltage between the R wave and the S wave.
(b) The P-R time interval.
(c) The Q-R-S time interval.
(d) The Q-T time interval.
(e) The frequency of your heart during data collection (in beats/min and in Hz)?

Briefly describe the exercise that was completed.  What effect did the exercise have on your EKG?
What things seemed unaffected?

If you have time for some extra lab credit:

Measure the electrical potential of a Bicep Muscle

When measuring an EKG, students are told to sit completely still.  Why?
Test what happens to the voltage signal when you flex your bicep while connected to the muscle leads vs. when relaxed.

Connect the positive and negative electrode to your subject's upper biceps as shown on the right.

Use a damp paper towel to wipe off the area at the top and at the bottom of the bicep muscle on the arm without an electrode on the wrist.

Firmly place electrodes on your skin so that you have 1 on your right wrist, 1 on the upper portion of the left bicep, and 1 on the lower portion of the left bicep (as pictured).

Connect the sensor to the electrodes.  The reference (black) lead should be connected to your wrist.  The red and green leads should be connected to the bicep muscle area.  Try to adjust the wires so that they are not twisting or pulling on the electrodes.

Prepare to collect data when the subject is relaxing his/her bicep muscle and when he/she is flexing the muscle.  A good technique for flexing the muscle is to lift up on the table.  Whether flexing or relaxing the muscle, try to stay as stationary as possible.

Describe the behavior of the data for this muscle and paste the graph into your log.

Experiment Deliverables: (to be included in the your journal)

• Visuals: 
  Your sketch of the electric field lines and equipotential curves across a human torso.
  Your predicted post-exercise trace over your resting trace.
  The graphs of your data resting and post-exercise and (optional) of the electric potential of the bicep muscle.
• Analysis:
  Explain why muscle depolarization velocity remains roughly constant while the pacemaker trigger rate changes between resting and exercise.
  Optional:  When you flex your bicep, how does the electrical signal of skeletal muscle contraction compare in amplitude and frequency to the heart's signal?  How does this explain 'artifacts' or noise in medical EKGs?
• Outcome:
  (a) - (e) resting and after exercise.
  Explain how you arrive at your answers.  You must justify all answers.

Activity

The concept of work

(a)  The work W done on an object by a constant force is defined as W = F∙d.  It is equal to the magnitude of the force, multiplied by the distance the object moves in the direction of the force.
The SI unit of work is Nm = J.
An object travels from point A to point B while two constant forces of equal magnitude are exerted on it, as shown in the figure on the right. 

• Is the work done on the object by F₁ positive, negative, or zero?  Why?
• Is the work done on the object by F₂ positive, negative, or zero?  Why?
• Is the net work done on the object positive, negative, or zero?  Why?

(b)  An object travels from point A to point B while two constant forces of unequal magnitude are exerted on it, as shown in the figure on the right. 

• Is the work done on the object by F₃ positive, negative, or zero?  Why?
• Is the work done on the object by F₄ positive, negative, or zero?  Why?
• Is the net work done on the object positive, negative, or zero?  Why?

Work and the electric field

In the diagram on the right, the red dot denotes a positive point charge.  Points W, X, Y, and Z and the point charge lie in the same plane.  Points W and Y are equidistant from the charge, as are points X and Z.
Draw the electric field vectors at points W, X, Y, and Z.
(c)  A particle with charge +q_e travels along a straight line from point W to point X.

• Is the work done by the electric field on the particle positive, negative, or zero?
  Explain using a sketch that shows the electric force on the particle and the displacement of the particle.

(d)  A particle travels from point X to point Z along the circular arc shown.

• Is the work done by the electric field on the particle positive, negative, or zero?  Explain!
  Hint:  Sketch the direction of the force on the particle and the direction of the displacement for several short intervals during the motion.

Electric potential difference

A potential energy function is a function of the position of an object.  It can only be defined for conservative forces.  A force is conservative if the work it does on an object depends only on the initial and final position of the object and not on the path. 
(e)  Suppose the moving charge in part (c) increases from +q_e to +1.8 q_e.

• Is the work done by the electric field as the particle travels from W to X greater than, less than, or equal to the work done by the electric field on the original particle.  Explain!
• How is the quantity "the work divided by the charge" affected by this change?

(f)  The electric potential difference  ∆V_WX between two points W and X is defined to be the negative of the work done by the electric field on a charge q, divided by q, as q travels from W to X.

• Does this quantity depend on the magnitude of the charge that is used?  Explain!
• Does this quantity depend on the sign of the charge that is used?  Explain!

When a net force does work on an object, its kinetic energy changes.
W_net = ½m(v_f² - v_i²) = ∆K.
(g)  A particle of charge |q_e| = 2*10^-6 C and mass m = 3*10^-8 kg is released from rest at point W.  The speed of the particle is measured to be 25 m/s as it passes point X. 

• Is q_e positive or negative?  Explain!
• What is the change in the kinetic energy of the particle as it travels from point W to point X?
• Find the work done on the particle by the electric field between points W and X.
• What is the electric potential difference ∆V_WX = V_W - V_X between points W and X?

(h) Review this 3-dimensionl representations of the equipotential surfaces of a charged sphere.
Equipotential surfaces of a charged sphere
Do this 3D representations help you visualize equipotential surfaces?

Assume you have a test charge at rest at a distance of 2 cm from the charge on the right.  You want to move it.

What path could you choose, so you would not have to do any work?   What is the shape of the equipotential surface?   (Remember that in general you can move in three dimensions.)  Explain your reasoning.

(i)  Find some equipotential surfaces for the charge configuration shown on the right, which consists of two charged metal plates placed parallel to each other.

What is the shape of the equipotential surfaces?  Remember you are trying to decide how a test charge could move so that the electric field does no work on it.  Sketch your predictions and explain your reasoning.

(j)  Before opening any simulation, sketch what you think the lines of equal electric potential look like around a dipole.  Why did you choose this shape?  (Don't worry if it is not perfect - this is your hypothesis!).  Now, open the 3D visualization link.
Field lines and equipotential surfaces 
How does your prediction compare to reality?
What changes if you choose two positive or two negative charges?

Activity 1 Deliverables: (to be included in the your journal)

• Analysis: 
  Answer all questions from sections (a) - (j).  When asked for sketches, include them.

Convert your journal into a lab report.  See the grading scheme for all lab reports.

Name:
E-mail address:

Laboratory 2 Report

• Make sure you completed the entire lab and answered all parts.  Make sure you show your work and inserted and properly labeled relevant tables and plots in your journal.
• Add a summary reflection at the end of your report in a short essay format.

Save your Word document (your name_lab2.docx), go to Canvas, Assignments, Lab 2, and submit your document.