Two identical charges repel each other with a force of 10-5 N when they are 20 cm apart.
a.) What is the force on each when they are 5 cm apart?
b.) When they are 100 cm apart?
Assessment
a) When the charges are 5 cm apart, the force between them can be determined using Coulomb's Law. Since the charges are identical, we can calculate the force using the formula F = k(q^2/r^2), where k is the electrostatic constant, q is the charge, and r is the distance between them.
Now, since F is directly proportional to q^2 and inversely proportional to r^2, we can write the equation as follows:
F1/F2 = (q1^2/q2^2) * (r2^2/r1^2)
Since F1 is given as 10^-5 N, r1 is given as 20 cm, and r2 is given as 5 cm, we can calculate the force F2 as follows:
10^-5 N/F2 = (q1^2/q2^2) * (5 cm/20 cm)^2
Simplifying the equation, we get:
F2 = 10^-5 N / [(q1^2/q2^2) * (25/400)]
= 10^-5 N / [(q1^2/q2^2) * (1/16)]
= 10^-5 N / (q1^2/q2^2) * 16
Since the charges are identical (q1 = q2), the equation simplifies further:
F2 = 10^-5 N / 16
Therefore, the force on each charge when they are 5 cm apart is 10^-6 N.
b) When the charges are 100 cm apart, we can use the same formula as above:
F1/F3 = (q1^2/q3^2) * (r3^2/r1^2)
Since F1 is given as 10^-5 N, r1 is given as 20 cm, and r3 is given as 100 cm, we can calculate the force F3 as follows:
10^-5 N/F3 = (q1^2/q3^2) * (100 cm/20 cm)^2
Simplifying the equation, we get:
F3 = 10^-5 N / [(q1^2/q3^2) * (100/20)^2]
= 10^-5 N / [(q1^2/q3^2) * 25^2]
= 10^-5 N / (q1^2/q3^2) * 625
Since the charges are identical (q1 = q3), the equation simplifies further:
F3 = 10^-5 N / 625
Therefore, the force on each charge when they are 100 cm apart is 1.6 x 10^-8 N.
To solve this problem, we can use Coulomb's law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Coulomb's law can be expressed as:
F = k * (q1 * q2) / r^2
Where:
- F is the force between the charges
- k is the electrostatic constant (k = 9 x 10^9 N m^2/C^2)
- q1 and q2 are the magnitudes of the charges
- r is the distance between the charges
Let's solve the given questions step by step:
a.) What is the force on each when they are 5 cm apart?
1. First, we need to find the force between the charges when they are 20 cm apart using the given information:
- F1 = 10^-5 N (force when they are 20 cm apart)
- r1 = 20 cm (distance when the force is 10^-5 N)
2. Next, we can use Coulomb's law to find the force when they are 5 cm apart:
- r2 = 5 cm (distance when we want to find the force)
To solve for F2, we can set up a proportion using the inverse relationship between force and distance:
- F1 / r1^2 = F2 / r2^2
Now, plug in the values we know:
- 10^-5 N / (20 cm)^2 = F2 / (5 cm)^2
Simplifying the equation gives:
- F2 = (10^-5 N * (5 cm)^2) / (20 cm)^2
Calculating this expression will give us the force when the charges are 5 cm apart.
b.) When they are 100 cm apart?
Using the same approach, we can find the force when the charges are 100 cm apart using Coulomb's law. Plug the known values into the formula and simplify the equation to obtain the desired force.
By following these steps, you will be able to find the force between the charges at different distances.
1/4 the distance? must be 16 times as great.
4 times as far? must be 1/16 as much
F=kQq/distance^2
25
300