phys lab report

4/7/2021 UNT PHYS 2240 Lab ENG_PHYS_2 E&M_FALL_2020 - Alymjan Rejepov/Experiment 8: Magnetic Field in a Current Carrying Coil/Backgr…

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UNT PHYS 2240 Lab ENG_PHYS_2 E&M_FALL_2020 - Alymjan Rejepov/Experiment 8: Magnetic Field in a Current Carrying Coil/Background Information

Introduction

Content LA Thirteen - Jun 13, 2020, 1:07 AM CDT

In this experiment we are comparing changes in axial and radial magnetic field components as the position of a magnetic field sensor is moved through a current carrying coil. The position is recorded by a string attached to the Magnetic Field Sensor that passes over the Rotary Motion Sensor pulley to a hanging mass.

Content LA Thirteen - Jun 13, 2020, 1:07 AM CDT

Theory

Content LA Thirteen - Jun 13, 2020, 1:08 AM CDT

4/7/2021 UNT PHYS 2240 Lab ENG_PHYS_2 E&M_FALL_2020 - Alymjan Rejepov/Experiment 8: Magnetic Field in a Current Carrying Coil/Backgr…

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Axial and Radial Field

The Magnetic Field Sensor is able to record the axial and radial components of the magnetic field as shown in Figure 1. The axial component of the magnetic field is the field that points in the direction of the solenoids vertical axis. The radial component of the magnetic field is the portion of the field that points outward from the center to the walls of the solenoid and beyond. Along with the magnitude of each component, the sensor detects the direction of each field component. The direction is relative to the orientation of the sensor and is denoted with positive and negative values.

Figure 1. Visualization of magnetic field through the solenoid

Single Coil

For a coil of wire of negligible length, as shown in Figure 2, having radius R and N turns of wire, the magnetic field along the perpendicular axis through the center of the coil is given by

where is the permittivity of free space, N is the number of turns, R is the radius of the coil, I is the current through the coil, and x is the distance from the center of the coil.

Figure 2: Single coil of Radius R

Long Solenoid (n coils)

For a long solenoid with n turns per unit length, the magnetic field is

where is the number of turns per unit length, and I is the current A through the solenoid.

Content LA Thirteen - Jun 13, 2020, 1:24 AM CDT

4/7/2021 UNT PHYS 2240 Lab ENG_PHYS_2 E&M_FALL_2020 - Alymjan Rejepov/Experiment 8: Magnetic Field in a Current Carrying Coil/Backgr…

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The direction of the field is straight down the axis of the solenoid. To be considered "long", the length of the coil must be much longer that the diameter of the coil as shown in Figure 3. In addition, Equation 2 will begin to fail when the ends of the solenoid are approached and the magnetic field strength will begin to decrease.

Figure 3: Long Solenoid

Short Solenoid

For the short solenoid on the AC/DC Electronics Laboratory, neither Equation 1 nor Equation 2 is correct since the coil is too long for Equation 1 to work and too short to use Equation 2. However, both equations tell us something about the behavior of the magnetic field. Both equations should yield upper bound values for the magnetic field at the exact center of the coil, since in the first case squeezing the 600 turns into zero length would make all of the coils closer and in the second case adding more coils would clearly increase the field. The specifications for the coil used in this experiment can be found in Table 1.

Table 1: Specifications for the Short Solenoid

Number of Turns 600 turns

Radius 1.5 cm

Length 2.5 cm