What would the slope of the force between 2 charged particles vs 1/r^2 give me?

Thread starter dannolul
Start date Apr 30, 2024
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Force Inverse Slope

In summary, the slope of the graph plotting the force between two charged particles against \(1/r^2\) represents the proportionality constant in Coulomb's law, which quantifies the strength of the electrostatic force. A linear relationship indicates that the force is inversely proportional to the square of the distance between the charges, consistent with the principles of electrostatics.

Apr 30, 2024

dannolul

Homework Statement: A lab was performed by taking 2 charged particles at varying distances and measuring the force between them. (Dry data, and a graph of Fe vs 1/r^2 have been given.) Assume the charges are equal of magnitude. using the slope of the line and the value of coulomb's constant constant, calculate for the charge on one particle

Relevant Equations: Fe=(kq1q2)/(r^2)

I can get the slope of the line, but then I dont know what the slope is (units or whatever it is) then i get lost from there.

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May 1, 2024

Ibix

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What did you plot on the ##y## axis and in what units? What did you plot on the ##x## axis and in what units? If the gradient of a ##y##-versus-##x## plot is ##\Delta y/\Delta x## then can you determine the units in this case?

FAQ: What would the slope of the force between 2 charged particles vs 1/r^2 give me?

What does the slope of the force between two charged particles vs 1/r^2 represent?

The slope of the force between two charged particles plotted against 1/r^2 indicates how the force varies with the distance between the particles. In electrostatics, the force between two point charges is described by Coulomb's law, which states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them. A linear relationship on this plot suggests that the force behaves according to the inverse square law.

How can I determine the slope from experimental data?

To determine the slope from experimental data, you would collect measurements of the force between two charged particles at various distances. By plotting these values with force on the y-axis and 1/r^2 on the x-axis, you can use linear regression analysis to find the best-fit line. The slope of this line will give you the proportionality constant that relates the force to 1/r^2.

What is the significance of a positive or negative slope?

A positive slope indicates that the force increases as the value of 1/r^2 increases, which is consistent with the behavior of attractive forces between opposite charges or repulsive forces between like charges. A negative slope would be indicative of an unusual relationship that does not conform to Coulomb's law, suggesting that the forces are not behaving as expected, possibly due to experimental error or additional forces acting on the particles.

Can the slope provide information about the nature of the charges?

Yes, the slope can provide insights into the nature of the charges. If the slope is consistent with Coulomb's law, it suggests that the charges are point charges and that the interaction follows the expected electrostatic principles. If the slope deviates significantly from the expected value, it may indicate that the charges are not point-like, or that other forces (such as magnetic or gravitational forces) may be influencing the interaction.

What units will the slope have in this context?

The slope of the plot of force versus 1/r^2 will have units that combine the units of force and the units of distance squared. Since force is typically measured in newtons (N) and distance in meters (m), the slope will have units of newtons per meter squared (N/m²). This unit reflects the proportionality constant in Coulomb's law that relates the force between charges to their separation distance squared.