(Someone please help me !! I don't understand this.)
Two tiny conducting spheres are identical and carry charges of -27.3C and +61.0C. They are separated by a distance of 2.64 cm. (a) What is the magnitude of the force that each sphere experiences? (b) The spheres are brought into contact and then separated to a distance of 2.64 cm. Determine the magnitude of the force that each sphere now experiences.
a. coulombs law
b. The touch, so charge is added, and now equal on each: Charge on each=1/2 (61-27.3) C. Then coulombs law again.
To solve this problem, we can use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of their separation distance.
(a) To find the magnitude of the force that each sphere experiences when they are at a distance of 2.64 cm, we can use Coulomb's Law formula:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the force
k is Coulomb's constant, approximately 8.99 × 10^9 N m^2/C^2
|q1| and |q2| are the charges of the spheres
r is the separation distance between the spheres
Substituting the given values into the formula, we have:
F = (8.99 × 10^9 N m^2/C^2) * (27.3C) * (61.0C) / (0.0264m)^2
Calculating this expression will give us the magnitude of the force each sphere experiences.
(b) When the spheres are brought into contact and then separated to a distance of 2.64 cm, their charges are redistributed. Since they are identical, they will have equal charges.
To determine the magnitude of the force each sphere now experiences, we can again use Coulomb's Law. The charges are now equal, so we can represent them as q.
F = k * (|q| * |q|) / r^2
Since they have equal charges, we can rewrite the formula as:
F = k * (|q|^2) / r^2
We can substitute the value of q and r into the formula to calculate the magnitude of the force.
It's important to note that in both cases, it's assumed that the spheres are small enough so that their separation distance is much larger compared to their sizes. Therefore, we can use the point charge approximation in Coulomb's Law.