Experiment 22The Current BalanceAdvanced Reading:(Serway) Chapter 29,sections 29-1 through 28 -4Equipment:1 Pasco Current Balance apparatus1 Dial-o-gram balance1 power supply3 double-banana plugwires.1 Kelvin DMM

Objective:

The objective of this lab isto measure the effects of amagnetic field on a currentcarrying conductor.

Theory:

A magnetic field FB exerts aforce on a moving positivecharge that is given by thevector cross product:

†

FB = qv ¥ B

Where q is the charge, v is thevelocity of the charge and B is themagnetic field strength.

The magnitude of this force is givenby:

FB = q vBsinq

where q is the smaller angle betweenthe velocity vector v and themagnetic field vector B.

Since a current is a collection ofcharges in motion, a magnetic fieldshould also exert a force on a current

carrying conductor. The magnitudeand direction of this force isdependent upon four factors: (1) thelength of the wire, (2) the strength ofthe magnetic field, (3) the magnitudeof the current, and (4) the anglebetween the field and the wire. Themagnetic force FB in this case is givenby the vector cross product:

FB =iL x B

figure 22-1

Current Limiting Resistor

A

Wire LoopVariablepowersupply

figure 22-2 Circuit diagram

where I is the current, L is the lengthof the wire, and B is the strength ofthe magnetic field.

Procedure :

Part 1: Force vs. Current

1. Set-up the apparatus as it appears infigure 21-1 and figure 21-2 using thecurrent loop numbered SF 42. Thecircuit consists of a power supply, anammeter (DMM) and the wire loop allconnected in series.

Before placing the magnet on thedigital balance, the balance should bezeroed. Push the “zero” button once.

2. Place the long magnet on the centerof the balance pan. The wire loopshould be arranged so that it passesthrough the pole region of the magnet(i.e., the horizontal part of the wire isjust below the top of the magnet). SeeFigure 21-3 below

Figure 22-3

3. Measure the mass of the longmagnet with no current flowing andcalculate its weight in newtons. This isyour zero force, F0 or zero weight, W0.

Once the experiment starts, donot move the setup. It is alsoimportant to keep all metalobjects and wires away from themagnet. These could affect thedata.

4. Before plugging in the powersupply, have your instructorcheck the circuit. After it has beenapproved, plug in the power supplyand adjust the dial until the DMM readsapproximately 1.0 amps. . When thecurrent is turned on, the magnetshould be deflected downwards. Readthe new mass from the balance andcalculate the weight F in newtons. Itshould be greater than it was when nocurrent is flowing. If the balancereads less than before, reversethe wires on the arm of thecurrent balance. The difference inthe weight with the current on, andwith the current off is the force due tothe magnetic field, FB. ( i.e., FB=F - F0 )Calculate this force.

5. Increase the current in 1.0 ampincrements until 5.0 amps is reached.Record the current and the magneticforce for each step. Using GraphicalAnalysis plot magnetic force vs.current and determine the best-fitline. Record the number on the side ofthe wide magnets. From the slope youwill determine the magnetic field ofyour magnet.

Part 2: Force vs. Length of Wire

6. For this part of the lab you will needto know the effective length of thewire loops. They are as follows:

SF 40 1.2 cmSF 37 2.2 cmSF 39 3.2 cmSF 38 4.2 cmSF 41 6.4 cmSF 42 8.4 cm

Note that the numbers on theloops do not signify the length ofthe wire.

Insert the shortest wire segment (SF40) into the holder. Measure the massof the magnet holder and the magnetsagain and determine its weight. (Itshould be about the same as before).

7. Adjust the power supply until theDMM reads 2.0 amps. Determine themagnetic force. Repeat for all six wireloops. Plot magnetic force vs. wirelength. . From the slope you willdetermine the magnetic field of yourmagnet.

Part 3: Force vs. Angle

8. Plug the Current Balance Accessoryinto the arm of the current balance.Replace the long magnet assemblywith the small “square” magnet. SeeFigure 21-4. Measure the mass. This isyour zero current mass. 9. Set the angle to 0o with thedirection of the coil wire parallel to themagnetic field. See Figure 21-5. Set thecurrent to 2.0 amps. Re-measure themass. If the mass changes, slightlyvary the angle of the magnet setup sothat the mass is as close as possible tothe zero current mass. Determine theforce. This force is your zero (angle)force, F0.10. Increase the angle in 10oincrements up to 180o. At each anglerepeat the magnetic forcemeasurement. Plot magnetic force vs.angle. From this plot, determine thestrength of the “square” magnet.

Questions/Conclusions:

1. What is the relationship betweenthe current and the magnetic force?

2. What is the relationship betweenthe length of the wire and themagnetic force?

3. What is the shape of the curve inpart 3? Sketch the shape of the curveif you could rotate the current balanceaccessory a full 360 degrees.

4. Show F=qvBsinq and F=iLBsinq aredimensionally equivalent.

5. Calculate the field strength of thewide magnets using the slope of thegraph in part 1. Write the number ofthe wide magnet you had. Your labinstructor has the correct values.

Figure 22-4

Figure 22-5