A +2 uC and a +10 uC are 3cm apart
a) Find the electrostatic force between the charges
b) If the charges are brought together and touched, what would be the charge on each one?
c) These spheres are then moved 3 cm apart. What would be the force between them?
What is the question on a) Coulombs law
b) the charge equalizes IF the SPHERES are the same size. 6 microC each
c. Again, Coulombs law.
Notice you don't have to do much math on c). the difference between a and c is the numerator, in a) you have 20, and in c you have 36.
So the force in c is 36/20 force in a.
To find the electrostatic force between two charges, you can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Let's take a look at each question:
a) To find the electrostatic force between the charges, you need to use Coulomb's Law, which can be expressed as:
F = k * (|q1| * |q2|) / r^2
Where:
F is the electrostatic force between the charges
k is Coulomb's constant (8.99 x 10^9 N m^2/C^2)
|q1| and |q2| are the magnitudes of the charges
r is the distance between the charges
In this case, |q1| = 2 uC (microcoulombs) and |q2| = 10 uC, and r = 3 cm. However, it's important to convert the values to SI units before calculating:
|q1| = 2 x 10^-6 C
|q2| = 10 x 10^-6 C
r = 3 x 10^-2 m
Substituting the values into the formula:
F = (8.99 x 10^9 N m^2/C^2) * ((2 x 10^-6 C) * (10 x 10^-6 C)) / (3 x 10^-2 m)^2
Simplifying:
F = 119.88 N
So, the electrostatic force between the charges is approximately 119.88 N.
b) When the charges are brought together and touched, they will equilibrate and share charge. The resulting charge on each sphere can be calculated using the principle of conservation of charge. The total charge before touching is the sum of the magnitudes of the charges, which is 2 uC + 10 uC = 12 uC. Since they are touched and come into equilibrium, the total charge after touching will still be 12 uC. Therefore, each sphere will have a charge of 6 uC.
c) After the spheres are moved 3 cm apart, we can use Coulomb's Law again to calculate the force between them. The charges remain the same, but the distance has changed. We need to convert the distance to SI units:
r = 3 cm = 3 x 10^-2 m
Using the same formula as in part a) but with the new distance:
F = (8.99 x 10^9 N m^2/C^2) * ((2 x 10^-6 C) * (10 x 10^-6 C)) / (3 x 10^-2 m)^2
Simplifying:
F = 9.99 N
So, the force between the charges when they are 3 cm apart is approximately 9.99 N.