Two identical positive charges exert a repulsive force of 6.6 multiplied by 10^-9 N when separated by a distance of 5.8 multiplied by 10^-10 m. Calculate the charge of each.
To calculate the charge of each positive charge, we can use Coulomb's Law:
F = k * q1 * q2 / r^2,
where:
- F is the force between the charges,
- k is Coulomb's constant (8.99 × 10^9 N m^2 / C^2),
- q1 and q2 are the charges of the two identical positive charges, and
- r is the distance between the charges.
In this case, we are given:
- F = 6.6 × 10^-9 N and
- r = 5.8 × 10^-10 m.
Plugging these values into the equation, we can solve for q1 and q2.
6.6 × 10^-9 N = (8.99 × 10^9 N m^2 / C^2) * q1 * q2 / (5.8 × 10^-10 m)^2.
Simplifying:
6.6 × 10^-9 N = (8.99 × 10^9 N m^2 / C^2) * q1 * q2 / (3.364 × 10^-19 m^2).
Cross multiplying:
6.6 × 10^-9 N * (3.364 × 10^-19 m^2) = (8.99 × 10^9 N m^2 / C^2) * q1 * q2.
Rearranging the equation:
(8.99 × 10^9 N m^2 / C^2) * q1 * q2 = (6.6 × 10^-9 N) * (3.364 × 10^-19 m^2).
Dividing both sides by (8.99 × 10^9 N m^2 / C^2):
q1 * q2 = (6.6 × 10^-9 N) * (3.364 × 10^-19 m^2) / (8.99 × 10^9 N m^2 / C^2).
Simplifying:
q1 * q2 = 2.482 × 10^-28 C^2.
To find the charge of each positive charge, we need to take the square root of both sides:
√(q1 * q2) = √(2.482 × 10^-28 C^2).
Taking the square root:
q1 = q2 = √(2.482 × 10^-28 C^2).
Calculating q1 and q2:
q1 = q2 ≈ 4.98 × 10^-14 C.
Therefore, the charge of each positive charge is approximately 4.98 × 10^-14 C.
To calculate the charge of each positive charge, we can use Coulomb's Law. Coulomb's Law states that the force between two charged particles 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,
k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2),
q1 and q2 are the charges of the particles, and
r is the distance between the particles.
In this case, we're given:
F = 6.6 x 10^-9 N
r = 5.8 x 10^-10 m
Substituting these values into Coulomb's Law, we get:
6.6 x 10^-9 N = (8.99 x 10^9 N m^2/C^2) * (q1 * q2) / (5.8 x 10^-10 m)^2
Simplifying the equation:
6.6 x 10^-9 N = (8.99 x 10^9 N m^2/C^2) * (q1 * q2) / (5.8 x 10^-10 m)^2
Rearranging the equation to solve for q1 * q2:
(q1 * q2) = (6.6 x 10^-9 N * (5.8 x 10^-10 m)^2) / (8.99 x 10^9 N m^2/C^2)
Calculating the right side of the equation:
(q1 * q2) = (3.876 x 10^-27 C^2) / (8.099 x 10^-10 C^2)
(q1 * q2) = 4.788 x 10^-18 C^2
Now, since both charges are identical, we can simplify and write:
q1^2 = 4.788 x 10^-18 C^2
Taking the square root of both sides:
q1 = √(4.788 x 10^-18 C^2)
Calculating q1:
q1 = 2.19 x 10^-9 C
Therefore, each positive charge has a charge of 2.19 x 10^-9 C.