Two point charges are separated by 6.4 cm. The attractive force between them is 10 N. Suppose that the charges attracting each other have equal magnitude. Rearrange Coulomb's law and find the magnitude of each charge
yes
14N
Coulomb's law is given by:
F = k * (|q1| * |q2|) / r^2
where:
F is the magnitude of the attractive force between the charges,
k is the electrostatic constant (which has a value of approximately 8.99 x 10^9 N m^2/C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the separation between the charges.
We are given that the attractive force (F) is 10 N and the separation (r) is 6.4 cm (which is equivalent to 0.064 m).
Let's rearrange the equation to solve for the magnitude of each charge (|q1| and |q2|):
F * r^2 = k * (|q1| * |q2|)
|q1| * |q2| = (F * r^2) / k
|q1| * |q2| = (10 N * (0.064 m)^2) / (8.99 x 10^9 N m^2/C^2)
Simplifying:
|q1| * |q2| = 4.096 x 10^-7 C^2
Since the charges have equal magnitude, we can write:
(|q1|)^2 = 4.096 x 10^-7 C^2
|q1| = √(4.096 x 10^-7 C^2)
|q1| ≈ 6.4 x 10^-4 C
Therefore, the magnitude of each charge is approximately 6.4 x 10^-4 C.
To find the magnitude of each charge, we can rearrange Coulomb's law equation:
F = k * (|q1| * |q2|) / r^2
where:
F is the force between the charges (10 N in this case),
k is the electrostatic constant (9 x 10^9 N*m^2/C^2),
q1 and q2 are the magnitudes of the charges, and
r is the separation between the charges (6.4 cm, which we'll convert to meters).
Step 1: Convert the separation distance from centimeters to meters:
r = 6.4 cm = 6.4 * 10^(-2) m = 0.064 m
Step 2. Rearrange Coulomb's law equation:
|q1| * |q2| = (F * r^2) / k
Step 3. Substitute the given values into the equation:
|q1| * |q2| = (10 * 0.064^2) / (9 * 10^9)
Step 4. Calculate the product of the charge magnitudes:
|q1| * |q2| = 4.096 / (9 * 10^9) C^2
Step 5. Take the square root of both sides to find the magnitude of each charge:
|q1| = sqrt(4.096 / (9 * 10^9)) C
Since the problem states that the charges have equal magnitudes, |q2| will also have the same value:
|q2| = |q1|
Now, we can evaluate the expression for |q1|:
|q1| = sqrt(4.096 / (9 * 10^9)) C
Calculating this expression will give us the magnitude of each charge.