Two point charges are separated by 9 cm, with
an attractive force between them of 18 N.
Find the force between them when they are
separated by 20 cm. The Coulomb constant
is 8.99 × 109 N · m2
/C
2
.
Answer in units of N.
To find the force between the two point charges when they are separated by 20 cm, we can use Coulomb's Law.
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.
Mathematically, it can be expressed as:
F = k * (q1 * q2) / r^2
where:
F is the force between the charges,
k is the Coulomb constant (8.99 × 10^9 N · m^2/C^2),
q1 and q2 are the charges of the two point charges, and
r is the distance between the charges.
Given that the force between the charges is 18 N when they are separated by 9 cm, we can set up the following equation:
18 N = (8.99 × 10^9 N · m^2/C^2) * (q1 * q2) / (0.09 m)^2
Now, we need to find the force when they are separated by 20 cm. Substituting this value into the equation, we have:
F = (8.99 × 10^9 N · m^2/C^2) * (q1 * q2) / (0.20 m)^2
Simplifying this expression, we get:
F = (8.99 × 10^9 N · m^2/C^2) * (q1 * q2) / 0.04 m^2
To find the force, we need to determine the product of the charges (q1 * q2). Since the question does not provide the specific value of the charges, we cannot provide an exact answer. However, you can calculate the force by plugging in the values of the charges into the equation:
F = (8.99 × 10^9 N · m^2/C^2) * (q1 * q2) / 0.04 m^2
Make sure to convert the charges to Coulombs and the distance to meters before doing the calculation.
To find the force between two point charges when they are separated by a different distance, you can use Coulomb's Law.
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. Mathematically, it can be expressed as:
F = k * (q1 * q2) / r^2
where F is the force between the charges, k is the Coulomb constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
Given:
Initial separation distance (r1) = 9 cm
Force between the charges (F1) = 18 N
We can use the given information to find the product of the charges (q1 * q2).
To find the force between the charges when they are separated by a different distance (r2), we can use the formula:
F2 = k * (q1 * q2) / r2^2
We need to substitute the known values into the equation:
F2 = (8.99 × 10^9 N · m^2 / C^2) * (q1 * q2) / (20 cm)^2
Now, let's solve for the product of the charges (q1 * q2).
(q1 * q2) = (F1 * r1^2) / (k)
Substituting the known values:
(q1 * q2) = (18 N * (9 cm)^2) / (8.99 × 10^9 N · m^2 / C^2)
Simplify the equation:
(q1 * q2) = 1458 cm^2 / (8.99 × 10^9 N · m^2 / C^2)
To get rid of the units in the denominator, convert cm^2 to m^2:
(q1 * q2) = (1458 cm^2 * (1 m^2 / 10000 cm^2)) / (8.99 × 10^9 N · m^2 / C^2)
(q1 * q2) = 0.1458 m^2 / (8.99 × 10^9 N · m^2 / C^2)
(q1 * q2) = 1.618 × 10^-11 C^2
Now, substitute the value of (q1 * q2) into the equation for F2:
F2 = (8.99 × 10^9 N · m^2 / C^2) * (1.618 × 10^-11 C^2) / (20 cm)^2
Convert cm to meters:
20 cm = 0.20 m
F2 = (8.99 × 10^9 N · m^2 / C^2) * (1.618 × 10^-11 C^2) / (0.20 m)^2
Now, calculate the value of F2:
F2 ≈ 4572 N
Therefore, the force between the two charges when they are separated by 20 cm is approximately 4572 N.