
Concept explainers
Two small spheres are given identical positive charges. When they are 1 cm apart, the repulsive force acting on each of them is 0.002 N. What would the force be if (a) the distance is increased to 3 cm? (b) one charge is doubled? (c) both charges are tripled? (d) one charge is doubled and the distance is increased to 2 cm?
(a)

The force between two small spheres if the distance is increased to 3 cm.
Answer to Problem 16E
The force if the distance is increased to 3 cm is 0.00022 N.
Explanation of Solution
Given data:
Formula used:
Consider the expression for the electrostatic force between two charges.
Here,
Substitute
Solve the equation to find
Substitute
Conclusion:
Hence, the force if the distance is increased to 3 cm is 0.00022 N.
(b)

The force between 2 small spheres if one of the charge is doubled.
Answer to Problem 16E
The force between 2 small spheres if one of the charge is doubled is 0.004 N.
Explanation of Solution
Substitute
Solve the equation to find
Since one of the charge is doubled, multiply 2 on both sides.
Substitute
Conclusion:
Hence, the force between two small spheres if one of the charge is doubled is 0.004 N.
(c)

The force between 2 small spheres if both of the charges are tripled.
Answer to Problem 16E
The force between 2 small spheres if both of the charges are tripled is 0.018 N.
Explanation of Solution
Substitute
Solve the equation to find
Since both of the charges are tripled, multiply
Substitute
Conclusion:
Hence, the force between 2 small spheres if both of the charges are tripled is 0.018 N.
(d)

The force between 2 small spheres if one charge is doubled and the distance is increased to 2 cm.
Answer to Problem 16E
The force between 2 small spheres if one charge is doubled and the distance is increased to 2 cm is 0.001 N.
Explanation of Solution
Substitute
Solve the equation to find
Since one of the charge is doubled, multiply 2 on both sides.
Substitute
Conclusion:
Hence, the force between two small spheres if one charge is doubled and the distance is increased to 2 cm is 0.001 N.
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