two small conducting spheres have charge 2nc and -0.5nc respectively. When they are placed 4 cm apart ,what is the force between them. If they are brought into contact and then seperated by 4cms. What is the force between them?
a. F=kq1q2/distance squared.
b. if they touch, the now charge on each is (2nq-.5)/2=.75nq
To calculate the force between the two small conducting spheres, 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.
Step 1: Calculate the electric charge in coulombs
Given that the charge of the first sphere is 2 nC (nanoCoulombs) and the charge of the second sphere is -0.5 nC, we need to convert these values to Coulombs. Recall that 1 nC = 1 × 10^-9 C.
Charge of the first sphere = 2 nC = 2 × 10^-9 C
Charge of the second sphere = -0.5 nC = -0.5 × 10^-9 C (note that a negative charge indicates an excess of electrons)
Step 2: Calculate the distance in meters
The spheres are placed 4 cm apart. To use Coulomb's Law, we need to convert this distance to meters. Recall that 1 cm = 0.01 m.
Distance between the spheres = 4 cm = 4 × 0.01 m = 0.04 m
Step 3: Calculate the force between the spheres
Using Coulomb's Law, the formula for the force (F) between two charged objects is:
F = (k * q1 * q2) / r^2
Where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between the two objects.
Coulomb's constant (k) = 8.99 × 10^9 N m^2/C^2
Plugging in the values:
F = (8.99 × 10^9 * (2 × 10^-9) * (−0.5 × 10^-9)) / (0.04)^2
F = (8.99 × 2 × (-0.5)) / 0.0016
F = -0.00359875 / 0.0016
F = -2.2498 N (rounded to four decimal places)
Therefore, the force between the two spheres is approximately -2.2498 Newtons.
If the spheres are brought into contact and then separated by 4 cm again, their charges redistribute, and the net charge on both spheres becomes the average of their initial charges.
Average charge = (2 nC - 0.5 nC) / 2 = 0.75 nC / 2 = 0.375 nC = 0.375 × 10^-9 C
Using the same formula and substituting this new charge value, along with the distance of 0.04 m, you can calculate the new force between the spheres.