A negative charge of -2.0x10 °C and a positive charge of 8.0x10 * Care separated by 0.30 m . What is the force between the two charges ?
F = k Q1 Q2 / d^2 (opposite charges attract each other.)
k = 9 * 10^9 N m^2/Coulomb^2
To calculate the force between two charges, we can use Coulomb's law equation:
F = k * (|Q1| * |Q2|) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2),
|Q1| and |Q2| are the magnitudes of the charges,
r is the distance between the charges.
Let's plug in the given values:
|Q1| = -2.0 x 10^(-6) C (negative charge)
|Q2| = 8.0 x 10^(-6) C (positive charge)
r = 0.30 m
F = (8.99 x 10^9 Nm^2/C^2) * ((|-2.0 x 10^(-6) C| * |8.0 x 10^(-6) C|) / (0.30 m)^2)
F = (8.99 x 10^9 Nm^2/C^2) * (2.0 x 10^(-6) C * 8.0 x 10^(-6) C) / (0.30 m)^2)
F = (8.99 x 10^9 Nm^2/C^2) * (16 x 10^(-12) C^2) / (0.09 m^2)
Performing the calculation:
F = (8.99 x 10^9 Nm^2/C^2) * (16 x 10^(-12) C^2) / (0.09 m^2)
= 1.597 x 10^(-3) N
Therefore, the force between the two charges is approximately 1.597 x 10^(-3) N.
To calculate the force between two charges, we can use Coulomb's law, which states that the force (F) between two charges (q1 and q2) is equal to the product of their charges divided by the square of the distance between them, multiplied by a constant called the Coulomb's constant (k).
Mathematically, Coulomb's law is represented as:
F = (k * |q1 * q2|) / r^2
where:
- F is the force between the charges,
- k is the Coulomb's constant (9.0 × 10^9 N*m²/C²),
- q1 and q2 are the two charges,
- r is the distance between the charges.
In the given problem, we have:
- q1 = -2.0 × 10^-6 C (negative charge)
- q2 = 8.0 × 10^-6 C (positive charge)
- r = 0.30 m (distance between the charges)
Substituting these values into Coulomb's law, we can calculate the force:
F = (9.0 × 10^9 N*m²/C²) * |(-2.0 × 10^-6 C * 8.0 × 10^-6 C)| / (0.30 m)^2
First, let's calculate the product of the charges:
|(-2.0 × 10^-6 C * 8.0 × 10^-6 C)| = 16.0 × 10^-12 C² = 1.6 × 10^-11 C²
Next, let's calculate the square of the distance:
(0.30 m)^2 = 0.09 m²
Now let's substitute these values back into the equation:
F = (9.0 × 10^9 N*m²/C²) * (1.6 × 10^-11 C²) / (0.09 m²)
Now we can simplify and calculate the force:
F = 9.0 × 10^9 N*m²/C² * 1.6 × 10^-11 C² / 0.09 m²
F = 1.44 × 10^-2 N
Therefore, the force between the two charges is 1.44 × 10^-2 Newtons.