Ampere's Law
Purpose:
To investigate Ampere's Law by measuring how magnetic field varies over a
closed path; to examine how magnetic field depends upon current.
Apparatus:
Solenoid and path integral board, DC power supply with builtin
voltmeter/ammeter, cables, Hall Effect magnetic sensor,
meter stick
Introduction
Ampere's Law states that the line integral of
B
and d
l
over a closed path is
0
times the
current enclosed in that loop:
∮
B
⋅
dl
=
0
I
enclosed
You have seen the usefulness of the law in determining, without complicated integration,
the magnetic field merely by knowing the currents enclosed by
a path with a high degree
of symmetry, such as a circular loop around a long straight wire.
For such a wire, the
magnetic field is given by:
B
long straight wire
=
0
I
2
R
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View Full Document(For a long straight wire carrying current I the B field line direction is tangent to centered
circles.
Along those circles, B is constant, so we can “pull it out of the integral”.
The
remaining integral is simply the circumference of the circle, which is
2
R
, so
B
long straight wire
⋅
2
R =
0
I
)
In your experiment,
I
must be understood as NI
multimeter
since the single wire of the
solenoid contributes I to the enclosed current with each winding (turn) of the solenoid) :
∮
B
⋅
dl
=
0
N I =
0
N I
multimeter
in general.
Equation 1
If there is no
net
current within the closed path, the closed integral is zero.
This does not
necessarily mean there is no B field present along the line integral, or no currents
enclosed.
Rather it means that the dot product with the field direction sums to zero.
Note
that “Up” and “down” currents through the enclosed surface must be assigned
opposite signs.
Think of two adjacent wires with equal and opposite currents. The closed line integral
surrounding them is zero.
If the closed line integral is not zero, you know that there is a
net
current within the closed path which is generating a magnetic field.
In this lab you
will actually sum up the contributions of
B ·
d
l
over such a path around a solenoid, to
check if their sum does indeed equal
0
times the current enclosed by your path.
The
magnetic field around the solenoid will be determined by a magnetic sensor; you will
measure the output voltage of the sensor (which is proportional to B) using the Fluke
multimeter.
The current through the solenoid will be measured by the readout on the
power supply.
SOLENOIDS
An
application of Ampere’s Law involves a solenoid (a wire coil wound on a cylinder)
with:
N = number of turns of solenoid (dimensionless)
R = radius of coil (meters)
I
multimeter
= current through solenoid (amperes)
L = length of solenoid (meters).
The B field intensity at the center
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 Fall '11
 Gilman
 Current, Power, Magnetic Field, power supply

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