electric field

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Apr 3, 2024

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1 Investigation of Electric Fields Assignment Zaryan Syed Physics (SPH4U) Mrs. Kennedy March 12, 2024

2 Pre-Laboratory Activity:

3 Testable Question How is the magnitude of the electric field affected by the distance from the source? Independent Variable Distance Dependent Variable Magnitude Control Variable Charge Hypothesis If the distance between the source and where the magnitude of the electric field is taken increases, then the strength of the electric field decreases. This can be explained by Coulomb's law equation (Physics Classroom, n.d.). The law states that the magnitude of the electric field strength is inversely proportional to the square distance of the source. Coulomb’s equation is expressed as: ε = k × Q / R 2 Where k represents Coulombs constant (8.99 × 10 9 N ⋅ m 2 / C 2 ) and q representing point charge in coulombs and r representing radius in meters, this equation shows that if the distance from the course is increased, the denominator of the equation will become larger, causing the quotient to become smaller, this relationship can be expressed as follows: ε ∝ 1 / 𝑅 2 Therefore, Based on Coulombs law, as the distance from the source of the electric field is increased, the denominator of the of the equation (R 2 ) will become larger, causing the overall electric field to decrease.

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4 Materials  Measuring tape  Electrometer  Charged rod  Metal Sphere  Metal wire Procedure 1. A metal sphere with no charge was placed on a lab space. 2. A positively charged rod was placed close to the metal ball, but not in contact with it. 3. A metal wire was connected to the sphere and the rod to transfer the charge. 4. The metal wire and rod were then removed after 30 seconds. 5. The measuring tape then measured 1 meter from the metal ball, the recorded measurement was entered into a raw data table. 6. The electrometer was placed 1 meter from the metal ball and recorded the electric potential energy, the recorded value was entered into a raw data table. 7. Electric field strength was calculated using raw data, and the results were entered into a calculated table. 8. Steps 5-7 were repeated for 2 meters, 3 meters, and 4 meters. Observations It was challenging to determine the most precise measurement since the sensor was quite sensitive to variations in range in terms of the magnitude of the field shown. The further the distance of the electrometer to the positively charged ball. The less electric potential there was, which when doing the calculations, made the electric field smaller. To create a constant reference, the metal ball charge was interpreted as +1 nC. Results Table 1- Measured values for distance vs charge of Electric Potential Trial Radius (m) Electric Potential (V)

5 1 1.00 8.981 2 2.00 4.515 3 3.00 3.010 4 4.00 2.254 Sample calculations: Magnitude of Electric Field (Theoretical) Electric Field (Trial 1): Recall: 1nC = 1 × 10 -9 , k = (9×10 9 ) Given: r = 1.00 m ε = k × Q / R 2 ε = (9×10 9 ) (1×10 -9 ) / 1.00 2 ε = 9.00 N/C Sample calculations: Magnitude of Electric Field (Measured) Electric Field (Trial 1): ε = V / R ε = 8.981 / 1.00 ε = 8.98 V/m 1 V/m = 1 N/C ε = 8.98 N/C Table 2- Calculated values for Magnitude of Electric Field Trial Measured Electric Field (N/C) Theoretical Electric Field (N/C) 1 8.98 9.00 2 2.26 2.25

6 3 1.10 1.00 4 0.56 0.56 1 2 3 4 0 1 2 3 4 5 6 7 8 9 10 8.98 2.26 1.10 0.56 Distance vs Electric Field Distance (m) Magnitude of Electric Field (N/C) Discussion: The strength of the electric field is dependent on the magnitude of distance from the source charge (The Physics Classroom). Charged items produce electric fields, which act as a force field on nearby charged objects. The strength of the force per unit of charge is measured by the electric field's magnitude. Because the electric field obeys the inverse-square rule, its magnitude diminishes with increasing distance from the source. Coulomb’s law expresses that the force of attraction between two charged points is proportional to the product of their charges and inversely proportional to the square of the distance between them which is why it was used in this experiment. Electric Field depends on the distance from the change, and its size gets smaller as the separation from the source increases. The link between the electric field's strength and the source's distance was evident in the experiment's results, which showed a distinct pattern and trend. The electric field's magnitude dropped with increasing distance. Across all assessed distances, this tendency held true. This is further shown in in the scatterplot graph, where the data exponentially decreases as distance

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7 increases. This graph demonstrates that the magnitude of the electric field decreases according to the inverse-square rule. Furthermore, the percent discrepancy difference between the theoretical value and the measured value is very small, with trial 3 having the biggest percent difference of 9.5%. Therefore, the hypothesis of the magnitude of Electric Field decreasing as distance increases is held true. Although the lab was conducted in a simulation, which meant that there were no outside influences on the experiment, external factors like inaccurate or miscalibrated instruments that are not sensitive enough to get an accurate reading or small variations in measurements due to human error would add to a margin of error if the exact procedure were carried out in a less than controlled environment. Similarly, not knowing the specific charge of the metal ball can create deviation from expected results since the values gained are expected if the ball was 1nC. Additional precautions would need to be taken to prevent such influences, including utilizing an automated measuring device that can take accurate measurements at specific intervals along with using a measuring tool to accurately determine the charge of the metal sphere. Conclusion: The investigation aimed to find a link between the electric field's strength and the source's distance. Through the results, the trend was shown that the magnitude of the electric field decreases as distance increases. Furthermore, the electric field was inversely proportional to the square of the distance from the charged object which is down through how the diagram is inversely exponential. Overall, this experiment proved the hypothesis that as distance from the source increased, the electric field magnitude decreased. References

8 The Physics Classroom. “Classroom Tutorial: Electric Field Intensity.” Physicsclassroom.com, 2019, www.physicsclassroom.com/class/estatics/Lesson-4/Electric-Field-Intensity

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