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Chapter 21: Problem 11

If two charged particles (the charge on each is \(Q\) ) are separated by a distance \(d\), there is a force \(F\) between them. What is the force if the magnitude of each charge is doubled and the distance between them changes to \(2 d ?\)

Short Answer

Expert verified
Answer: The force between the two charged particles remains the same.

Step by step solution

01

Identify the formula for calculating force between two charged particles

Coulomb's law is used to calculate the electrostatic force between two charged objects. The formula of Coulomb's law is: F = k * (|q1 * q2|) / r^2, where F is the force between the charges, k is the electrostatic constant (8.99 * 10^9 N m^2 / C^2), q1 and q2 are the magnitude of the charges, and r is the distance between the charges.
02

Input the given values into the formula

We have two charged particles with charge Q each and separated by distance d. The force between them is F. Substitute the given values into the formula: F = k * (|Q * Q|) / d^2.
03

Calculate the force for the changed conditions

Now, the magnitude of each charge is doubled, and the distance between them changes to 2d. Let's denote the new force by F'. Substitute the new values into the formula: F' = k * (|(2Q) * (2Q)|) / (2d)^2.
04

Simplify the new force equation

Simplify the equation for the new force F': F' = k * (4 * Q^2) / (4 * d^2). Next, we can simplify this expression by dividing the numerator and denominator by 4: F' = k * (Q^2) / (d^2).
05

Compare the original force with the new force

Now let's compare F and F' to find the relationship between the original force and the new force: F = k * (Q^2) / (d^2), F' = k * (Q^2) / (d^2). As we can see, F and F' are equal, meaning that the force between the charged particles remains the same when the magnitude of each charge is doubled and the distance between them is changed to 2d. So, the force between the two charged particles remains F under the new conditions.

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Most popular questions from this chapter

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