202L-Sp 2001-(T.Arshed, C.Erkal)

Experiment #5: The Magnetic Force on a Current-Carrying
Wire.

When a current (I) carrying conductor is placed at right angles to a magnetic field (B), it experiences a force F perpendicular to both I and B. The magnitude of the force on a length (L) of conductor is given by

**F = B L I** (1)

In this experiment, you will place a conductor
between the poles of a magnet that rests on an ordinary laboratory
balance. When no current flows through
the conductor the balance simply measures the weight W_{o} of the
magnet. When a *properly directed* current flows through the conductor, a magnetic
force, give by Eq. (1), acts on the conductor [and by Newton’s third law also
acts on the magnet]. You can choose the direction of current flow such that the
magnetic force will add to the magnet’s weight. Thus the “weight” W recorded by
the balance is given by

**W = (B L) I + W _{o} **

This is just like the
equation of a straight line: Y = aX + b. You can record the balance reading W
for several different currents I, then plot a graph of W (y-axis) versus I
(x-axis). This should be a straight line with the slope of the line as (BL) and
its intercept as W_{o}. As you are given the length L, from the slope
you can determine B. The intercept should represent W_{o}. Here, the
calculations are done by the computer program **MAGFORCE** that performs a least squares fit to the (I,W) data
points. It will yield, not only the slope and intercept of the best possible
straight line but also the error in these.

**EQUIPMENT:**

1 – Power Supply 1 – 3 ohm power resistor 1 – current balance 1 – dc ammeter |
1 -- Dial-O-Gram balance 1 -- magnetic assembly 1 -- conductor with known length
-- clip leads |

**PROCEDURE:**

1. Make
sure the power supply is not plugged in and the switch is turned off.

*2.
*Place
the magnet on the balance pan. Lower
the current balance until the * horizontal segment* of the conductor
is between the magnet’s poles.

3. Hook
up the circuit shown in the figure. The
current flows out of the + (red) terminal of the power supply, into the + 3A
(red) terminal of the ammeter, out of the COM ammeter terminal and into one arm
of the current balance. From there the
current flows through the conductor, out the other arm of the current balance,
through the power resistor and finally back to the – (black) terminal of the
power supply.

4. Go
over your circuit carefully again before proceeding.

5. Weigh
the magnet with no current flowing. Record as W_{o}.

6. Plug
in and turn on the power supply. On your table are given values of current to
work with.

7. Adjust
the current to the first value specified at your lab table. The current should be flowing through the
conductor so as to increase the “weight”.
This is so if the conductor wire in the magnetic field shows a downward
movement. If it moves upward, the current is flowing in the wrong direction.
Simply *reverse* the leads connected to
the current balance.

8. Balance
the scale and record the “weight” W.

9. Repeat
steps 7 – 8 for *the other* current
values listed. This should complete one set of (I, W).

10. Repeat
steps 7 – 9 two more times so that you have a total of three sets for *each* given current.

**COMPUTER
WORK:**

Use the Excel spreadsheet MAGFORCE to analyze
your data. MAGFORCE will do this:

ü
Convert your grams (g) measurements to weight W
in newtons (N).

ü
Calculate the average weight W and its standard
deviation from the 3 trials for *each*
current.*

ü
Perform a least squares best fit to the average
“weight” W versus current I data and print the slope and intercept of the
best-fit line.

ü
From the slope, determine the magnetic field B
and its standard deviation.

ü
Perform certain auxiliary calculations.

**GRAPH
and CALCULATIONS:**

1. Plot
your data points for average “weight” W versus current I. Do not join the
points. Show *s*_{W
}as error bars on W values.

2 On the back of the printout, rewrite, *in proper form*, your value for the
slope, intercept and magnetic

field together with
the errors, from the printout.

3. Write the equation of the best-fit line using this slope and intercept in the form Y = aX + b.

Choose two values of X and determine their Y coordinates from the equation of the best-fit line. Show work.

4. Plot the two points you calculated in (3) above. Place triangles around them. Join the two points to get the best-fit line through your data points. [Label all info. Your graph should conform to the usual guidelines].

3. Choose two points A and B, farthest apart on your graph line and using these, determine the slope and the intercept of your line.

4. Calculate the magnetic field B from the
slope. If *s*_{L
}is given as ±1
mm, calculate *s*_{B}.

5. *Check *the intercept value from your
computer printout, with the measured _{} (weighing on the
balance)* for consisten*cy. The error
on the balance can be ignored. Show work.

6. Staple together
your data sheet, printout, graph and calculations and place in the orange box.