### Electric potential and EKG measurements

In this studio session 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.

Equipment needed:

EKG sensor

Electrode patches

Rubbing alcohol

Open a Microsoft Word document to keep a log of your experimental procedures,
results and discussions. This log will become your lab report. Address the
points highlighted in blue. Answer all questions.

**Equipotential Surfaces**

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 or an external force doing any work, then the
surface is called an **equipotential surface**.

**Activity 1**

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.

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.

Find some equipotential surfaces for the electric
dipole charge configuration shown on the right.

Sketch your predictions and explain your
reasoning.

**Activity 2**

Use a spreadsheet to calculate the electric potential at grid
points in the in the x-y plane due to 1, 2, 3, or 4 small, uniformly-charged
spheres. The x-y plane is divided into a 25 x
25 grid. The upper left corner of the grid corresponds to x = 0.5 m, y =
0.5 m, and the lower right corner corresponds to x = 24.5 m, y = 24.5 m.
The charged spheres can be placed anywhere on the grid. They will be
located in the x-y plane. The spreadsheet calculates the potential at each
grid point and produces a surface and a contour plot of the potential.

The potential at **r **= (x,y,z) outside a uniformly
charged sphere centered at **r**’ = (x’,y’,z’) is

V(**r**)
= kq/|**r **- **r**'| = kq/((x - x')^{2} + (y - y')^{2} + (z -
z')^{2})^{1/2}.

In the x-y plane we have z = 0 and

V(x,y) =
kq/((x - x')^{2} + (y - y')^{2})^{1/2}.

The constant k has a value of 9*10^{9} in SI
units. If we measure q in units of nC = 10^{9 }C, then kq = 9*q Nm^{2}/C

Download this Microsoft Excel spreadsheet.

Examine the spreadsheet

Calls B1 -Z1 contain the x-coordinates and cell A2 - A26 the
y-coordinates of the grid points

Cells A31 - C34 contain the x- and y-coordinates (in
units of m) of the positions and the magnitudes (in units of nC) of four
charges.

The spreadsheet initializes with a +10 nC charge at x =
13 m, y = 13 m and all the other charges have zero magnitude.

(**When
you add more charges, let the x- and y-coordinates always be integers.
This avoids “divide by zero” errors, since the grid points have half
integer x- and y-coordinates.**)

Cell B2 contains the formula

=9*$C$31/SQRT((B$1-$A$31)^2+($A2-$B$31)^2)

+9*$C$32/SQRT((B$1-$A$32)^2+($A2-$B$32)^2)

+9*$C$33/SQRT((B$1-$A$33)^2+($A2-$B$33)^2)

+9*$C$34/SQRT((B$1-$A$34)^2+($A2-$B$34)^2)

This is the sum of
V(x,y) = kq/((x - x')^{2} + (y - y')^{2})^{1/2} due to the four charges.

Cell B2 is copied into the other cells of the
grid. The grid consists of cells B2 - Z26.

The spreadsheet shows two plots of the potential at
the grid points. The contour lines are equipotential lines. ** They are
spaced in 5V intervals**.

(a) Start with just the one +10 nC charge at x = 13 m, y = 13 m.

Describe the graphs.
What do they tell you about the potential outside a uniformly charged sphere?
Can you get information about the electric field outside a uniformly charged
sphere from these graphs, i.e. can you draw field lines? Estimate the
magnitude and direction of the electric field in units of V/m = N/C at x = 20 m,
y = 13 m.

(b) Now change the positions and
magnitudes of your charges. Use the numbers below.

x |
y |
q |

10 |
13 |
10 |

16 |
13 |
10 |

0 |
0 |
0 |

0 |
0 |
0 |

Just type in the new numbers into the cells
A31 - C34 and the spreadsheet and the graphs will update automatically.

Describe your graphs. What do they tell you about the potential of this charge distribution?

(c) Again change the positions and
magnitudes of your charges. Use the numbers below.

x |
y |
q |

10 |
13 |
10 |

16 |
13 |
-10 |

0 |
0 |
0 |

0 |
0 |
0 |

Describe your graphs. What do they tell you about the potential of this charge distribution?

(d) Again change the positions and
magnitudes of your charges. Use the numbers below.

x |
y |
q |

10 |
10 |
10 |

16 |
10 |
-10 |

10 |
16 |
-10 |

16 |
16 |
10 |

Describe your graphs. What do they tell you about the potential of this charge distribution?

(e) again change the positions and
magnitudes of your charges. Use the numbers below.

x |
y |
q |

10 |
10 |
20 |

16 |
10 |
-10 |

10 |
16 |
-10 |

16 |
16 |
20 |

Describe your graphs. What do they tell you about the potential of this charge distribution?

**Experiment**

You will now use the PASCO EKG sensor to measure the action potential of your
heart.

Link:
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.

Connect the EKG sensor unit to analog channel A of
the Pasco 850 interface box using the cable with the
DIN connectors.

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

In the Capstone program, click the Hardware Setup button on the left
and add a Science Workshop Analog Sensor. Chose the EKG
sensor. Click Hardware Setup again to close this window.

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 log.

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

**Analyzing your data**

Using your data, answer the following questions for your heart.
Explain how you arrive at your answers. You must justify all
answers.

(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 logbook. Explain any differences that may
occur due to this change.

**Collecting more data**

EKG after mild exercise

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, answer the following questions
for your heart. Explain how arrive at your answers. You must justify all answers.

(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**

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.

**Data Analysis**

Describe the behavior of the data for this
muscle and paste the graph into your log. Are you convinced
that this muscle generates a voltage when it is flexed?
Explain!

How is the signal from the bicep muscle
similar to or different from the signal from the heart muscle?

Convert your log into a session report, certify with you signature that
you have actively participated, and hand it to your instructor.