Two positive charges one 2uc and the other 7uc are separated by a distance of 20cm, what is the magnitude of the electrostatic force that each charge exerts upon the other
Homework
q=+5uc-d=4cm-q=7uc
To calculate the magnitude of the electrostatic force between two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
F is the force
k is the electrostatic constant, approximately equal to 9 * 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, we have two charges: q1 = 2 μC and q2 = 7 μC. The distance between them is r = 20 cm = 0.2 m.
First, let's convert the charges to units of Coulombs:
1 μC = 10^-6 C
So, q1 = 2 μC = 2 * 10^-6 C and q2 = 7 μC = 7 * 10^-6 C.
Now, let's substitute these values into the formula:
F = (9 * 10^9 N*m^2/C^2) * ((2 * 10^-6 C) * (7 * 10^-6 C)) / (0.2 m)^2
Simplifying further:
F = (9 * 10^9 N*m^2/C^2) * (14 * 10^-12 C^2) / (0.04 m^2)
F = (9 * 10^9 N * 14 * 10^-12 C^2) / (0.04 m^2)
F = (126 * 10^-3 N) / (0.04 m^2)
F ≈ 3.15 * 10^-3 N
Therefore, the magnitude of the electrostatic force that each charge exerts upon the other is approximately 3.15 * 10^-3 N.
To find the magnitude of the electrostatic force that each charge exerts on the other, you can use Coulomb's Law. Coulomb's Law states that the magnitude of the electrostatic force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
Where:
- F is the magnitude of the electrostatic force
- k is Coulomb's constant (k = 9 × 10^9 N m^2/C^2)
- q1 and q2 are the charges of the two objects
- r is the distance between the charges
In this case, q1 = 2 μC (microCoulombs) and q2 = 7 μC. The charges need to be converted to Coulombs, so 1 μC = 1 × 10^(-6) C.
Therefore, q1 = 2 × 10^(-6) C and q2 = 7 × 10^(-6) C.
The distance between the charges, r, is given as 20 cm. However, it must be converted to meters, so r = 0.2 m.
Now we can substitute these values into the formula:
F = (9 × 10^9 N m^2/C^2) * ((2 × 10^(-6) C) * (7 × 10^(-6) C)) / (0.2 m)^2
Calculating this equation will give us the magnitude of the electrostatic force.