two equally charged spheres, X and Y, repel each other with a force of 8.0 x 10^-6 N when placed a certain distance apart. Another identical, but uncharged, sphere is touched to sphere Y and then moved next to sphere X. Calculate the electric force acting on sphere Y.
let the initial charges be X,Y
Final charges will be (X+Y/2)(Y/2)
net force: (3/2)(1/2)original force or new force is 3/4 of the original.
To calculate the electric force acting on sphere Y after it is touched by the uncharged sphere and moved next to sphere X, we need to understand the concept of electrostatics and Coulomb's law.
Coulomb's law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The equation for Coulomb's law is:
F = k * (q1 * q2) / r^2
Where:
- F is the electric force between the charges,
- k is the electrostatic constant (9 × 10^9 N m^2/C^2),
- q1 and q2 are the charges of the two objects, and
- r is the distance between the centers of the spheres.
In this case, the two initially equally charged spheres X and Y repel each other with a force of 8.0 x 10^-6 N. Since they repel each other, it means they have the same type of charge (either both positive or both negative).
After the uncharged sphere is touched to sphere Y, it acquires the same charge as Y. Since the uncharged sphere gains charge from Y, the charge on sphere Y becomes zero while the uncharged sphere becomes equally charged as Y.
Now, when the charged sphere Y (with charge q2) is moved next to sphere X, the distance between the centers of spheres X and Y remains the same as before.
To find the electric force acting on sphere Y, we need to determine the charge on sphere X (q1). Since the spheres were initially equally charged, we can assume that the charge on sphere X is the same as that on sphere Y before it was touched by the uncharged sphere.
Now, we can use Coulomb's law to find the electric force (F) acting on sphere Y:
F = k * (q1 * q2) / r^2
Plug in the values:
F = (9 × 10^9 N m^2/C^2) * (q1 * q2) / r^2
Given that F = 8.0 x 10^-6 N, q2 = 0 (after being touched by the uncharged sphere), and r remains the same, we can simplify the equation to:
8.0 x 10^-6 N = (9 × 10^9 N m^2/C^2) * (q1 * 0) / r^2
Since q2 = 0, the electric force acting on sphere Y after the process is 0.