The force between two identical charges separated by 1 cm is equal to 90 N. What is the magnitude of the two charges?
F=90
r=1cm=0.01m
k=8.99*10^9
90=(8.99*10^9)(q)^2/0.01m
0.9=(8.99*10^9)(q)^2
1.00*10^10=q^2
q=1.00*10^-5 or -1.00*10^-5
q = sqrt(F r^2/k)
just rearrange Coulomb's Law
F = k q1q2/r^2
Rearrange gives;
q = Fr^2/k
= (90)(0.01)^2/8.99 x 10^9
= 1 x 10^-12 C
Find the force of attraction between two equal but opposite charges, of 2x10 C if the distance between them is 25 cm.
Well, if you want to calculate the magnitude of the two charges, let's bring out the big guns... or should I say, the electric guns? Imagine two charges sitting there, 1 cm apart, pulling each other with a force of 90 N. That's some serious attraction!
Now, to find the magnitude of the charges, we can use Coulomb's Law, my electric friend. Coulomb's Law tells us that the force between two charges is directly proportional to the product of their magnitudes, divided by the square of the distance between them. Mathematically, it can be expressed as:
F = (k * |Q1| * |Q2|) / r^2
Where F is the force, k is a constant, |Q1| and |Q2| are the magnitudes of the charges, and r is the distance between them.
In this case, we know the force is 90 N, and the distance is 1 cm (which we need to convert to meters). Unfortunately, we don't know the value of k, but we can look it up. It's approximately equal to 9 x 10^9 N.m^2/C^2.
Armed with this knowledge, let's rearrange the equation to solve for the magnitude of the charges:
|Q1| * |Q2| = (F * r^2) / k
Plugging in the values, we get:
|Q1| * |Q2| = (90 N * (0.01 m)^2) / (9 x 10^9 N.m^2/C^2)
Simplifying this expression gives us:
|Q1| * |Q2| = 1 x 10^-9 C^2
Now, since we know the charges are identical (as mentioned in the question), we can say that |Q1| = |Q2| = Q, so:
Q^2 = 1 x 10^-9 C^2
Finally, taking the square root of both sides, we get:
Q = ±1 x 10^-4 C
So, the magnitude of each charge is 0.0001 C (or ±0.0001 C if you want to get fancy with the plus-minus sign).
Remember, though, that the values I've provided are based on the assumption that you're dealing with point charges and that there are no other factors affecting the force. But hey, I think it's pretty electrifying to calculate the magnitude of these charges, don't you?
To determine the magnitude of the charges, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Let's denote the magnitude of the charges as q. According to the given information, the force (F) between the two charges is 90 N, and the distance (r) between them is 1 cm, which is equivalent to 0.01 meters.
Using Coulomb's Law, we have the equation:
F = k * (q1 * q2) / r^2
where k is the electrostatic constant.
Substituting the given values, the equation becomes:
90 = k * (q * q) / (0.01)^2
To determine the magnitude of the two charges (q), we need to find the value of k. The electrostatic constant, denoted by k, is approximately equal to 9 x 10^9 Nm^2/C^2.
Substituting the value of k into the equation, we have:
90 = (9 * 10^9) * (q * q) / (0.01)^2
Simplifying further:
90 = (9 * 10^9) * q^2 / 0.01^2
Rearranging the equation, we obtain:
q^2 = (90 * 0.01^2) / (9 * 10^9)
Solving for q^2:
q^2 = 0.000000001
Taking the square root of both sides of the equation gives us:
q = sqrt(0.000000001)
Evaluating the square root:
q ≈ 0.0000316
Hence, the magnitude of the two charges is approximately 0.0000316 C.