PHYSICS 127 EXPERIMENT NO. 7
MAGNETIC FORCE II
In this experiment a simple current balance will be used to measure the force
on a current-carrying wire in a magnetic field. The magnetic field is
produced by a solenoid, and from the magnitude of the force on the wire the
number of turns in the solenoid will be calculated.
A. Equipment
1 Power Supply, 1 Solenoid, 1 50A Current Shunt, 1 Digital Voltmeter,
1 Current Balance.
B. Method
The current balance is shown schematically in the following diagram:
I
Q
B
P
R
S
F
Weight
Solenoid
I
Figure 1. The Current Balance. Current flows from point P to point S through
the path PQRS. The solenoid's magnetic field in combination with the current
segment QR creates a downward force which is balanced by the weight.
The balance arm is a thin rectangular insulator upon which a conducting
wire PQRS is attached. The pins at P and S serve both a balance pivots and
current terminals for this wire. The balance arm is positioned so that the
wire segment QR is at the center of the solenoid. It is adjusted so that it
balances when no current passes through PQRS. When current flows in
such a direction as to pull the wire down, the force on the wire can be
measured by adding weights at W to counterbalance the magnetic force.
The wire segment and the solenoid are connected in series and each carries a
current I. The force on segment QR is given by:
F  BI  l
(1)
where l is the length of the segment QR and B is the magnetic field of the
solenoid. In the long solenoid approximation, the magnetic field B is given
by:
NI
L
(2)
where N is the total number of turns in the solenoid, and L is the length of
the solenoid (see pp. 726-727 in the 7th ed. or pp. 819-820 in the 8th ed. of
the text). The force on QR can then be written:
B  0
F  0
Nl 2
I
L
(3)
Q1. In what direction would F point if I were reversed:
(a) In the current balance and not in the solenoid?
(b) In both the current balance and the solenoid?
C. Procedure
Connect the solenoid and the wire PQRS in series in such a way that the
force on RQ will be down. You should decide beforehand how this
connection is to be made. Adjust the balance so that it is horizontal when no
current flows through the wire.
You will be supplied with several lengths of thin wire whose weight can be
determined. Hang one of these wires at the notches on the outer end of the
current balance. Turn up the solenoid/balance combination until balance is
achieved. Record the weight of the wire and the corresponding balance
current. Repeat the measurement several times to determine the uncertainty
in the balance current.
Repeat the above procedure with at least five other weights.
Q2. Plot the magnetic force as a function of the square of the balance current. Be
sure to show appropriate error bars for each point.
Q3. From the slope of the plot in Q2, find the number of turns in the solenoid,
Q4. In the derivation of equation (3), we did not consider the forces on wire
segments PQ and RS. Was this justified? Explain.
Q5. Does neglecting the forces on segments PQ and RS result in the value you got
for the number of turns being larger or smaller than the actual value? Explain.