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#### Lab Activities

In this lab, the students use a small search coil, an oscilloscope and Faraday's law of induction to measure and map the magnetic fields in a single coil and in a set of Helmholtz coils.

The specific lab activities are:

• to experimentally measure the magnitude of the magnetic field, Bo, at the center of a single coil

• to experimentally measure the magnitude of the magnetic field, Bo, at a point on the axis midway between the two coils of a set of Helmholtz coils

• to map the magnetic field strengths of a single coil and a set of Helmholtz coils along both their transverse and longitudinal axes

• to confirm that the emf induced in the search coil is 90 degrees out of phase with the current in the coils which is creating the fields

• to confirm that the emf induced in the search coil which has its longitudinal axis at an angle q to the direction of the uniform magnetic field is given by the expression

emf = wnBoAcos q

where w = the angular frequency of the ac current creating the field, n = the number of turns in the search coil, A = the cross sectional area of the search coil, Bo = the maximum magnetic field strength and q = the angle to which the search is turned to the direction of the field

• to make a rough estimate of the volume within a given set of Helmholtz coils in which the magnetic field is uniform

• to map the shape of the magnetic field of a single coil in a plane perpendicular to the plane of the coil and passing through the center of the coil.

In all cases, experimental results are compared to theoretical predictions. Experimental results tend to be within 2% of the expected results.

#### Equipment

 Number of set-ups available: 1 Per lab station: 1 oscilloscope 1 set of Helmholtz coils/banana leads 1 step-down transformer 1 search coil 1 wooden slotted peg 1 ruler 1 sheet of polar graph paper 4 banana leads 2 alligator clips 1 BNC to banana adapter (female)

#### Notes

 Last Update: Site contact: largent@Dartmouth.EDU