An object with a charge of 2.3 space x space 10 to the power of negative 6 end exponent C and an object of charge negative 4.2 space x space 10 to the power of negative 6 end exponent are .30 m apart. Calculate the magnitude of the force.
To calculate the magnitude of the force between two charged objects, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the force between two charged objects 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 force
k is the Coulomb's constant (approximately equal to 9 x 10^9 Nm^2/C^2)
q1 and q2 are the charges of the objects
r is the distance between the objects
Let's plug in the given values into the formula:
q1 = 2.3 x 10^(-6) C
q2 = -4.2 x 10^(-6) C
r = 0.30 m
F = (9 x 10^9 Nm^2/C^2) * (|2.3 x 10^(-6) C * -4.2 x 10^(-6) C|) / (0.30 m)^2
Now, we can calculate the magnitude of the force by substituting the values into the formula and performing the calculations:
F = (9 x 10^9 Nm^2/C^2) * (|2.3 x 10^(-6) C * -4.2 x 10^(-6) C|) / (0.30 m)^2
F = (9 x 10^9 Nm^2/C^2) * (2.3 x 10^(-6) C * 4.2 x 10^(-6) C) / (0.30 m)^2
F = (9 x 10^9 Nm^2/C^2) * (9.66 x 10^(-12) C^2) / (0.30 m)^2
F = (9 x 10^9 Nm^2/C^2) * (9.66 x 10^(-12) C^2) / 0.09 m^2
F = (9 x 10^9 Nm^2) * (9.66 x 10^(-12)) / 0.09
Performing the multiplication and division:
F = 8.688 x 10^(-3) N
Therefore, the magnitude of the force between the two objects is 8.688 x 10^(-3) Newtons.