# Investigating Magnetic Field Strengths: A Simple Physics Laboratory

Categories: Physics

In this laboratory experiment, we aim to explore the magnetic field strengths produced by various configurations of magnets and currents. Understanding magnetic fields is crucial in numerous scientific and technological applications, ranging from electromagnets to the functioning of everyday electronic devices. Through this practical investigation, we will employ basic principles, formulas, and calculations to quantify and compare the magnetic field strengths generated under different conditions.

Materials and Equipment:

1. Bar magnets (two or more)
2. Compass
3. Magnetic field sensor
4. Current-carrying wire
5. Power supply
6. Ruler
7. Paper and pen for recording observations

Procedure:

1. Measuring the Magnetic Field of a Bar Magnet: a.

Place the bar magnet on a flat surface. b. Use the compass to identify the magnetic poles of the bar magnet. c. Position the magnetic field sensor at a specific distance from the magnet and record the magnetic field strength. d. Repeat the measurements at different distances to observe the variation in magnetic field strength.

2. Effect of Magnetic Field Orientation: a. Reposition the magnet so that its orientation changes.

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b. Repeat the magnetic field strength measurements at the same distances as in step 1. c. Analyze the impact of the magnet's orientation on the magnetic field strength.

3. Magnetic Field Around a Current-Carrying Wire: a. Set up a simple circuit with a current-carrying wire. b. Place the magnetic field sensor at various distances from the wire.

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c. Record the magnetic field strength and observe the relationship between distance and field strength.

Calculations:

1. Magnetic Field Strength Calculation: The magnetic field strength (B) at a given point can be calculated using the formula: where:
• is the magnetic field strength,
• is the permeability of free space (),
• is the current flowing through the wire, and
• is the distance from the wire.
2. Analysis of Results: a. Create tables to organize the data collected from the magnetic field strength measurements. b. Graphically represent the data to observe trends and patterns.

In this laboratory, we investigated magnetic field strengths using basic setups involving bar magnets and current-carrying wires. The calculations provided insights into the relationship between magnetic field strength, distance, and current. Through this experiment, we gained a deeper understanding of the fundamental principles governing magnetic fields. These findings are essential not only in academic contexts but also for various applications in technology and industry.

In this section, we focus on the analysis and interpretation of the experimental results obtained from the investigation into magnetic field strengths. The dependent quantity in the table of results is the angle of deflection (𝛉).

Q2. Reversing Current to Obtain Opposite Angles: The decision to reverse the current in each measurement was a strategic approach to eliminate potential inaccuracies caused by the compass or external magnetic fields. By taking measurements with the current flowing in opposite directions, the effects of possible variables, such as interference from external magnetic fields or compass inaccuracies, were mitigated. This was exemplified by considering a scenario where the compass reading is initially 25° and affected by a 7° error. Reversing the current direction resulted in a new compass reading of -18°. Taking the average of these two values effectively canceled out the error, yielding a more accurate result.

Q3a. Plotting the Graph: To verify the expected relationship between , , and , Graph 1B was generated. The graph demonstrates a linear relationship between tan⁡ and 1/, supporting the theoretical relationship .

Q3b. Agreement with Theoretical Relationship: The graph exhibits a close linear relationship () between and , confirming that . The equation derived from the graph aligns with the theoretical relationship , where is a constant.

Q4. Equation of in Terms of : From the graph, the equation of in terms of is determined as (in meters).

Q6. Uncertainties in Measurements: Uncertainties in the measurement of distance and angle are inevitable. Parallax errors and limitations of the ruler contribute uncertainties of ±0.5 mm for distance and ±0.5° for angle. Adjustments made to the rheostat compensated for changes in current due to wire resistance, minimizing this factor's impact on uncertainties.

Q7. Calculating Earth's Magnetic Field Strength (): Comparing the experimentally determined equation to the theoretical one, is calculated using the gradient () obtained from the graph. The resulting is found to be .

Q8b. Discrepancy with Known Value of : The experimentally determined value of may differ from the known value due to the compass's constraint to a horizontal plane. The Earth's magnetic field has a 60° inclination at Brisbane, requiring vector addition to consider the vertical component (). The real value of is determined to be , accounting for this inclination.

Updated: Feb 26, 2024