Two electrostatic point charges of +30 μC and +25 μC exert a repulsive force of 200 N on each other. What is the distance between the two charges?
0.45
Well, it seems like those charges really don't want to be close to each other! They're like two magnets that repel each other whenever they come close. Anyway, let's figure out the distance between them.
We can use Coulomb's Law to solve this. Coulomb's Law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
So, let's plug in the given values into the formula:
Force = k * [(charge1 * charge2) / (distance^2)]
Given:
Force = 200 N
Charge1 = +30 μC
Charge2 = +25 μC
We can convert the charges to Coulombs by multiplying by 10^-6: Charge1 = +30 * 10^-6 C, Charge2 = +25 * 10^-6 C
Now we can rearrange the formula to solve for distance:
distance = sqrt((k * (charge1 * charge2)) / Force)
Plugging in the values:
distance = sqrt((k * ((+30 * 10^-6 C) * (+25 * 10^-6 C))) / (200 N)
But guess what? Clown Bot doesn't know the value of the constant 'k' in Coulomb's Law! So, I'm afraid I can't give you the exact distance between the charges.
But here's a tip: You can look up the value of 'k' (the Coulomb constant) and plug in all the given values to find the distance. Trust me, it'll be shocking!
To determine the distance between two charges, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
where F is the force between the charges, q1 and q2 are the charges, r is the distance between the charges, and k is the electrostatic constant.
Given:
Charge q1 = +30 μC
Charge q2 = +25 μC
Force F = 200 N
We can plug these values into Coulomb's Law to solve for the distance, r:
200 N = k * (30 μC) * (25 μC) / r^2
Now, we need to determine the value of k, the electrostatic constant. The value of k is 8.99 * 10^9 N m^2 / C^2.
Plugging in the values, we have:
200 N = (8.99 * 10^9 N m^2 / C^2) * (30 μC) * (25 μC) / r^2
To simplify the equation, we can convert the charges to coulombs:
30 μC = 30 * 10^-6 C = 3 * 10^-5 C
25 μC = 25 * 10^-6 C = 2.5 * 10^-5 C
Plugging in these values, we have:
200 N = (8.99 * 10^9 N m^2 / C^2) * (3 * 10^-5 C) * (2.5 * 10^-5 C) / r^2
Simplifying further:
200 N = (8.99 * 10^9 N m^2 / C^2) * (7.5 * 10^-10 C^2) / r^2
Now, we solve for r^2:
r^2 = (8.99 * 10^9 N m^2 / C^2) * (7.5 * 10^-10 C^2) / 200 N
r^2 = 3.37275 * 10^-6 m^2
Taking the square root of both sides gives us the distance, r:
r = √(3.37275 * 10^-6 m^2)
Calculating this value, we find:
r ≈ 0.001836 m
Therefore, the distance between the two charges is approximately 0.001836 meters.
To find the distance between the two charges, we can use Coulomb's Law, which relates the electrical force between two charges to the charge magnitudes and the distance between them. Coulomb's Law is given by:
F = k * |q1 * q2| / r^2
where:
F is the electrostatic force between the charges,
k is Coulomb's constant (k = 8.99 × 10^9 N * m^2 / C^2),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
In this case, we are given:
F = 200 N,
q1 = +30 μC = +30 × 10^-6 C, and
q2 = +25 μC = +25 × 10^-6 C.
To find the distance r, we rearrange Coulomb's Law equation:
r^2 = k * |q1 * q2| / F
Plugging in the values:
r^2 = (8.99 × 10^9 N * m^2 / C^2) * (|+30 × 10^-6 C * +25 × 10^-6 C| / 200 N)
r^2 = (8.99 × 10^9 N * m^2 / C^2) * (30 × 10^-6 C * 25 × 10^-6 C / 200 N)
r^2 = (8.99 × 10^9 N * m^2 / C^2) * (0.0075 × 10^-6 C^2 / 200 N)
Now, we can simplify the units:
r^2 = (8.99 × 10^9 N * m^2 / C^2) * (7.5 × 10^-9 C^2 / 200 N)
r^2 = (8.99 × 10^9 * 7.5 × 10^-9) (m^2) / (C^2 / N)
r^2 = 67.425 (m^2)
To find the distance r, we take the square root of both sides:
r = √67.425 m
Therefore, the distance between the two charges is approximately 8.20 meters.