The charges of two identical aluminum speheres are -24uC and +4.0uC. The spheres are brought together so they simultaneously touch each other. They then separated and placed on the X-axis. What is the net force exerted b one sphere on another after seperation?
add the charges, then divide the result by 2, that is the net charge on each.
Now, to compute the force, you need the radius of the spheres to get the separation.
To find the net force exerted by one sphere on the other after separation, 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 the distance between them.
Let's call the first sphere with a charge of -24 µC as sphere A, and the second sphere with a charge of +4.0 µC as sphere B.
Step 1: Calculate the electric force between the spheres when they are in contact.
When the spheres touch each other, they share charges until they reach equilibrium. This means that they will have equal and opposite charges.
Therefore, both sphere A and sphere B will end up with a charge of (-24 + 4.0) µC = -20 µC.
Step 2: Calculate the distance between the spheres when they are separated.
From the problem statement, it's mentioned that the spheres are placed on the X-axis. However, the distance between them is not specified. Let's assume that the distance between sphere A and sphere B after separation is 1 meter.
Step 3: Calculate the net force exerted by sphere A on sphere B after separation.
Using Coulomb's law, the formula for electric force (F) is:
F = (k * |q1 * q2|) / r^2,
where F is the force, k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2), q1 and q2 are the charges of the spheres, and r is the distance between them.
Substituting the values into the formula, we have:
F = (8.99 x 10^9 N m^2/C^2) * (|-20 µC * 4.0 µC|) / (1 m)^2
Calculating the equation gives us:
F = (8.99 x 10^9 N m^2/C^2) * (80 µC^2) / 1 m^2
F = 7.192 x 10^8 N
Therefore, the net force exerted by sphere A on sphere B after separation is 7.192 x 10^8 Newtons.