Two charged spheres P and Q have charges of+3C and -6C respectively.how far apart must the spheres be placed so that they exert an electrostatic force of 5 N on each other
To determine the distance between the charged spheres that would result in an electrostatic force of 5 N, we can use Coulomb's Law, which describes the relationship between the electrostatic force, the charges, and the distance between them.
Coulomb's Law states that the electrostatic force (F) between two charged objects is directly proportional to the product of their charges (q1 and q2) and inversely proportional to the square of the distance between them (r):
F = k * (|q1| * |q2|) / r^2
Where:
F is the electrostatic force
k is the electrostatic constant (k ≈ 9 × 10^9 N m^2/C^2)
q1 and q2 are the charges of the two spheres
r is the distance between the spheres
In this case, the charged spheres have charges of +3C and -6C. Substituting these values into Coulomb's Law, we get:
5 = (9 × 10^9 N m^2/C^2) * (|+3C| * |-6C|) / r^2
To simplify the equation, we can express the charges without their signs since their magnitudes will always be the same:
5 = (9 × 10^9 N m^2/C^2) * (3C * 6C) / r^2
Now, substituting the values and solving for r:
5 = (9 × 10^9 N m^2/C^2) * (18C^2) / r^2
To isolate r^2, we rearrange the equation:
r^2 = (9 × 10^9 N m^2/C^2) * (18C^2) / 5
Let's calculate the value of r:
r^2 = (9 × 10^9 N m^2/C^2) * (18C^2) / 5
r^2 = 3.24 × 10^10 m^2/C^2
r ≈ √(3.24 × 10^10 m^2/C^2)
r ≈ 5700 m
Therefore, the spheres must be placed approximately 5700 meters apart to exert an electrostatic force of 5 N on each other.
To find the distance between the two charged spheres, we can use Coulomb's Law, which states that the electrostatic force between two charged particles is given by:
F = (k * |Q1 * Q2|) / r^2
where:
F is the electrostatic force (5 N in this case),
k is the electrostatic constant (8.99 × 10^9 N·m^2/C^2),
Q1 and Q2 are the charges on the spheres (+3C and -6C, respectively),
and r is the distance between the spheres (which we need to find).
Let's start by rearranging the equation to solve for r:
r = √((k * |Q1 * Q2|) / F)
Substituting the given values:
r = √((8.99 × 10^9 N·m^2/C^2 * |3C * -6C|) / 5 N)
r = √((8.99 × 10^9 N·m^2/C^2 * 18C^2) / 5 N)
Now, we can simplify the equation:
r = √(8.99 × 10^9 N·m^2/C^2 * 18C^2) / √(5 N)
r = √(8.99 × 10^9 * 18) m / √5
r = √(161820000000) m / √5
Using a calculator, we can find the value:
r ≈ 20142.79 m
Therefore, the spheres must be placed approximately 20142.79 meters apart to exert an electrostatic force of 5 N on each other.