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. Be sure the conductor is not touching the sides or bottom of the magnet.

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 consistency. 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.