A small cork with an excess charge of +5.0 ¦ÌC
is placed 0.14 m from another cork, which
carries a charge of −3.2 ¦ÌC.
What is the magnitude of the electric force
between the corks? The Coulomb constant is
8.98755 ¡Á 109 N ¡¤ m2/C2.
Answer in units of N
To find the magnitude of the electric force between the corks, we can use Coulomb's Law, which states that the electric force between two charges is 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 magnitude of the electric force
k is the Coulomb constant (8.98755 × 10^9 N · m^2/C^2)
|q1| and |q2| are the absolute values of the charges
r is the distance between the charges
Plugging in the values from the problem:
|q1| = +5.0 μC = 5.0 × 10^(-6) C
|q2| = -3.2 μC = -3.2 × 10^(-6) C
r = 0.14 m
Substituting the values into the formula, we get:
F = (8.98755 × 10^9 N · m^2/C^2) * (|5.0 × 10^(-6) C| * | -3.2 × 10^(-6) C|) / (0.14 m)^2
Calculating this expression:
F = (8.98755 × 10^9) * (5.0 × 10^(-6)) * (3.2 × 10^(-6)) / (0.14)^2
F = 92.35 N
Therefore, the magnitude of the electric force between the corks is 92.35 N.
To find the magnitude of the electric force between the two charged corks, you can use Coulomb's Law, which states that the magnitude of the electric force between two point 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 given by:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the electric force between the charges,
k is the Coulomb constant (k = 8.98755 x 10^9 N · m^2/C^2),
|q1| and |q2| are the magnitudes of the charges (in this case, |q1| = 5.0 µC and |q2| = 3.2 µC),
r is the distance between the charges (in this case, r = 0.14 m).
Plugging in the values into the formula, we get:
F = (8.98755 x 10^9 N · m^2/C^2) * (|5.0 µC| * |-3.2 µC|) / (0.14 m)^2
Now, let's calculate it:
F = (8.98755 x 10^9 N · m^2/C^2) * (5.0 x 10^-6 C * 3.2 x 10^-6 C) / (0.14 m)^2
F = (8.98755 x 10^9 N · m^2/C^2) * (16 x 10^-12 C^2) / (0.0196 m^2)
F = 143.8036 N
Therefore, the magnitude of the electric force between the corks is approximately 143.8 N.