in an experiment using Coulomb's apparatus, a sphere with a charge of 3.6 x 10^-8 C is 1.4 cm from a second sphere of unknown charge. The force between the spheres is 2.7 x 10^-2 N. What is the charge of the second sphere?
I get 1.3 x 10^-4 C, but the answer is supposed to be 1.6 x 10^-8. Any possibility the book has a misprint? Where did I go wrong?
F = k Q1 Q2/r^2
k = 9*10^9
2.7 * 10^-2 = 9 * 10^9 * 3.6 * 10^-8 Q2/.014^2
Q2 = 1.63 * 10^-5 * 10^-3
= 1.63*10^-8 C
To calculate the charge of the second sphere, you can use Coulomb's law:
F = k * (q1 * q2) / r^2
Where:
F = force between the spheres
k = Coulomb's constant (k = 8.99 x 10^9 N•m^2/C^2)
q1 = charge of the first sphere (3.6 x 10^-8 C)
q2 = charge of the second sphere (unknown)
r = distance between the spheres (1.4 cm = 0.014 m)
Rearranging the equation, we have:
q2 = F * (r^2) / (k * q1)
Substituting the given values:
q2 = (2.7 x 10^-2 N) * (0.014 m)^2 / ((8.99 x 10^9 N•m^2/C^2) * (3.6 x 10^-8 C))
Simplifying the equation:
q2 = 1.55 x 10^-8 C
Therefore, the charge of the second sphere is approximately 1.55 x 10^-8 C.
It seems there was a mistake in your calculation. The correct answer should be 1.55 x 10^-8 C, not 1.3 x 10^-4 C.
To find the charge of the second sphere, you need to use Coulomb's law equation:
F = k * (q1 * q2) / r^2
Where:
- F is the force between the spheres (given as 2.7 x 10^-2 N)
- k is the electrostatic constant, approximately equal to 8.99 x 10^9 N m^2 / C^2
- q1 is the charge of the first sphere (given as 3.6 x 10^-8 C)
- q2 is the charge of the second sphere (what we need to find)
- r is the distance between the spheres (given as 1.4 cm or 0.014 m)
Rearranging the equation, we get:
q2 = (F * r^2) / (k * q1)
Now, let's substitute the given values and calculate:
q2 = (2.7 x 10^-2 N * (0.014 m)^2) / (8.99 x 10^9 N m^2 / C^2 * 3.6 x 10^-8 C)
Doing the math, you should get:
q2 ≈ 1.6 x 10^-8 C
So, your calculation is correct, and it seems like there may be a misprint in the book.