Concept explainers
Protons and electrons have different masses. When they are the same distance apart, the electric force between two electrons
- a. is less than the force between two protons
- b. is the same as the magnitude of the force between two protons
- c. is greater than the force between two protons
- d. Any of these choices could be correct, depending on the distance between each pair of particles.
To choose: The correct option from the given options.
Answer to Problem 4MC
The correct option is “b. is same as the magnitude of the force between two protons”.
Explanation of Solution
Given data:
Protons and electrons have different masses.
From the given data, it is required to compare the force between two electrons with respect to the force between two protons when the distance between two electrons is equal to the distance between two protons.
Formula used:
Refer to the equation (6-1) in the textbook, and write the expression for force between two electric charges as follows.
Here,
From equation (1), it is clear that, the force between two electric charges does not depend on the mass of the charges.
Consider the distance between two protons as
As the distance between two protons is same as distance between two electrons, the distance between two electrons is
In nature, the electric charge on a proton is
Calculation of force between two protons
Modify the expression in equation (1) for the force between two protons as follows.
Here,
Substitute
Simplify the expression as follows.
Calculation of force between two electrons
Modify the expression in equation (1) for the force between two electrons as follows.
Here,
Substitute
Simplify the expression as follows.
From equation (3), and (5), the force between two electrons is equal to the force between two protons. Therefore, the option b is an adequate option.
Since, force between two electrons is given as less than the force between two protons, the option a is incorrect answer.
Since, force between two electrons is given as greater than the force between two protons, the option c is incorrect answer.
From the analysis, the only option b is the correct choice. Therefore, the option d is absolutely incorrect.
Conclusion:
Hence, the correct option is “b. is same as the magnitude of the force between two protons”.
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Chapter 6 Solutions
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