What is the electric force between a glass ball that has +4.5 × 10−6 C of charge and a rubber ball that has −7 × 10−6 C of charge when they are separated by a distance of 4.9 cm? The value of the Coulomb constant is 8.98755 × 109 N · m2/C2.
To calculate the electric force between the two balls, we can use Coulomb's law, which states that the electric 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 is:
F = (k * |q1 * q2|) / r^2
Where:
F is the electric force between the two charges.
k is the Coulomb constant (8.98755 × 10^9 N·m^2/C^2).
q1 and q2 are the charges of the two balls.
|r| is the distance between the two balls (in this case, 4.9 cm or 0.049 m).
Plug in the given values:
F = (8.98755 × 10^9 N·m^2/C^2 * |4.5 × 10^-6 C * -7 × 10^-6 C|) / (0.049 m)^2
Calculate the absolute value inside the brackets:
F = (8.98755 × 10^9 N·m^2/C^2 * 3.15 × 10^-11 C^2) / (0.049 m)^2
Calculate the numerator:
F = 2.78501 N·m^2/C
Calculate the denominator:
(0.049 m)^2 = 0.002401 m^2
Now, divide the numerator by the denominator to find the electric force:
F = 2.78501 N·m^2/C / 0.002401 m^2
F ≈ 1160.68 N
Therefore, the electric force between the glass ball and the rubber ball is approximately 1160.68 N.
To find the electric force between two charged objects, we can use Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where:
F is the electric force between the objects,
k is the Coulomb constant (8.98755 × 10^9 N · m^2/C^2),
q1 and q2 are the charges on the objects,
|r| is the distance between the objects.
In this case, we have a glass ball with a charge of +4.5 × 10^−6 C, and a rubber ball with a charge of -7 × 10^−6 C. The distance between them is 4.9 cm, which can be converted to meters by dividing by 100 (1 cm = 0.01 m).
Let's calculate the electric force:
F = (8.98755 × 10^9 N · m^2/C^2 * |4.5 × 10^−6 C * -7 × 10^−6 C|) / (0.049 m)^2
First, let's multiply the charges:
|4.5 × 10^−6 C * -7 × 10^−6 C| = 4.5 × 10^−6 C * 7 × 10^−6 C = 3.15 × 10^−11 C^2
Now, let's substitute the values into the formula:
F = (8.98755 × 10^9 N · m^2/C^2 * 3.15 × 10^−11 C^2) / (0.049 m)^2
Next, let's calculate the square of the distance:
(0.049 m)^2 = 0.002401 m^2
Now, substitute the values:
F = (8.98755 × 10^9 N · m^2/C^2 * 3.15 × 10^−11 C^2) / 0.002401 m^2
Finally, let's divide and calculate the result:
F = 41.3496 N
Therefore, the electric force between the glass ball and the rubber ball is approximately 41.35 N.
F=k•q₁•q₂/r²
k =8.98755•10⁹ N•m²/C²