Q1 and Q2, when separated by a distance of 2 m, experience a force of repulsion eqaul to 1.8 N.(a) What will the force of repulsion be when they are 10 m apart?
(b) if the ratio Q1/Q2 = 1/2, find Q1 and Q2 ( r = 10m)
I want to know the answer
To solve this problem, we can use Coulomb's law formula for electric force between two point charges:
F = k * (Q1 * Q2) / r^2
where:
F is the force of repulsion,
k is the electrostatic constant (9 x 10^9 Nm^2/C^2),
Q1 and Q2 are the magnitudes of the two charges, and
r is the distance between the charges.
(a) What will the force of repulsion be when they are 10 m apart?
Given:
Initial distance between charges, r1 = 2 m
Initial force of repulsion, F1 = 1.8 N
New distance between charges, r2 = 10 m
We can set up a proportion using Coulomb's law:
F1 / F2 = (r1 / r2)^2
Using the given values:
1.8 N / F2 = (2 m / 10 m)^2
Simplifying:
1.8 N / F2 = 0.04
To find F2, we rearrange the equation:
F2 = 1.8 N / 0.04
Calculating:
F2 = 45 N
Therefore, when the charges are 10 m apart, the force of repulsion will be 45 N.
(b) If the ratio Q1/Q2 = 1/2, find Q1 and Q2 (r = 10 m)
Using the ratio given, Q1/Q2 = 1/2, we can solve for Q1 and Q2.
Let's assume Q2 = Q units.
From the ratio, we can say Q1 = (1/2) * Q = Q/2.
Using Coulomb's law, we know:
F = k * (Q1 * Q2) / r^2
Substituting the values, we get:
45 N = (9 x 10^9 Nm^2/C^2) * (Q/2 * Q) / (10 m)^2
Simplifying and solving for Q:
45 = (9 x 10^9) * (Q^2 / 2) / 100
(45 * 100) / (9 x 10^9) = Q^2 / 2
Q^2 = (45 * 100 * 2) / (9 x 10^9)
Q^2 = 10^(-6)
Taking the square root of both sides, we get:
Q = 10^(-3) C
Therefore, Q1 = Q/2 = 10^(-3) C / 2 = 5 x 10^(-4) C and Q2 = Q = 10^(-3) C.
To answer these questions, we need to understand the relationship between electric force and the distance between two charges, as well as the relationship between the electric force and the charge of the two particles.
(a) To find the force of repulsion when the charges are 10m apart, we can use Coulomb's Law, which states that the force between two charged particles is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The mathematical equation for Coulomb's Law is:
F = k * (Q1 * Q2) / r^2
where F is the force, Q1 and Q2 are the charges of the particles, r is the distance between them, and k is the electrostatic constant (which is approximately 9 * 10^9 Nm^2/C^2).
In this case, we know that when the charges are 2m apart, they experience a force of repulsion equal to 1.8N. So, we can substitute these values into the equation and solve for k:
1.8N = k * (Q1 * Q2) / (2m)^2
Simplifying this equation, we get:
1.8N = k * (Q1 * Q2) / 4m^2
Now, we can plug in the given values for k and solve for (Q1 * Q2):
1.8N = (9 * 10^9 Nm^2/C^2) * (Q1 * Q2) / 4m^2
Multiplying both sides of the equation by 4m^2 and dividing by 9 * 10^9 Nm^2/C^2, we get:
(Q1 * Q2) = (1.8N * 4m^2) / (9 * 10^9 Nm^2/C^2)
Using the given ratio Q1/Q2 = 1/2 in part (b), we can solve for Q1 and Q2.
Since Q1/Q2 = 1/2, we can write Q1 = (1/2) * Q2. Substituting this into the previous equation, we get:
(1/2) * Q2 * Q2 = (1.8N * 4m^2) / (9 * 10^9 Nm^2/C^2)
Multiplying both sides by 2 and rearranging the equation, we have:
Q2^2 = (2 * 1.8N * 4m^2) / (9 * 10^9 Nm^2/C^2)
Taking the square root of both sides, we can solve for Q2:
Q2 = sqrt((2 * 1.8N * 4m^2) / (9 * 10^9 Nm^2/C^2))
Finally, we can substitute this value back into Q1 = (1/2) * Q2 to find Q1.
Please note that you need to plug in the given values (such as 1.8N, 4m, and 9 * 10^9 Nm^2/C^2) into the equations to get the numerical values for Q1, Q2, and the force of repulsion.