8.1
Experiment 8
The Magnetic Field
Objectives
In this experiment, you will explore the magnetic field generated by current loops. You
will
• Measure the magnitude and direction of magnetic fields
• Apply Ampere’s Law to determine the magnetic field from a conductor
• Demonstrate that the Boit-Savart Law correctly predicts magnetic fields
• Confirm the behavior of Helmholz coils
Introduction
Historically, the magnetic field was first associated with natural permanent magnets. In
the development of the nineteenth century, electric and magnetic fields were connected – both
are produced by charges. Moving charges produce magnetic fields. (In fact, electric and
magnetic fields are a single electromagnetic field, but the object is a tensor. We find it easier to
treat E and B. It is the requirements of relativity on how the equations transform to moving
coordinates that creates a magnetic field from moving charges.) The equations for the source of
the magnetic field are Ampere’s Law and the Boit-Savart Law. (Both are consequences of the
fundamental Maxwell Equation for B.) In this experiment, we shall test several calculations
based on these laws.
Since current must flow in closed loops, the simplest laboratory configuration is a
circular loop. The magnetic field on the axis of the loop, a line through the center of the loop
perpendicular to the plane of the loop, is given by
!
Bz(z)=
µ
oNIR2
2R2+z2
( )
3 / 2
(1)
where R is the radius of the loop, z is the distance from the plane, and the loop has N turns of
wire with I. Note that the magnetic field points along the axis of the loop.
Another simple case is an infinitely long straight wire. Either Ampere’s Law or the Boit-
Savart Law may be used to determine that the magnetic field goes in circles around the wire with
a magnitude
!
B=
µ
oNI
2
"
r
(2)
