Investigating Magnetic Field Strengths: A Simple Physics Laboratory

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 $B$ , $I$ , and $d$ , Graph 1B was generated. The graph demonstrates a linear relationship between $tan θ$ and $1/ d$ , supporting the theoretical relationship $B \propto d 1$ .

Q3b. Agreement with Theoretical Relationship: The graph exhibits a close linear relationship ( $R^{2} = 0.997$ ) between $tan θ$ and $1/ d$ , confirming that $B \propto d 1$ . The equation derived from the graph aligns with the theoretical relationship $B I = K I / d$ , where $K$ is a constant.

Q4. Equation of $tan θ$ in Terms of $d$ : From the graph, the equation of $tan θ$ in terms of $d$ is determined as $tan θ = 7.36 \times 1 0^{-2} / d$ (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 ( $B_{E}$ ): Comparing the experimentally determined equation to the theoretical one, $B_{E}$ is calculated using the gradient ( $K$ ) obtained from the graph. The resulting $B_{E}$ is found to be $2.7 \times 1 0^{-5} T$ .

Q8b. Discrepancy with Known Value of $B_{E}$ : The experimentally determined value of $B_{E}$ 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 ( $B E_{H}$ ). The real value of $B_{E}$ is determined to be $2.7 \times 1 0^{-5} T$ , accounting for this inclination.