An enlightening image showcasing an illustration of two identical charges separated by a distance. The two charges are displayed at either end of the diagram in vibrant colors to represent their equal but opposite nature. A dotted line connects the charges to indicate the separation distance, subtly marked with a generic unit, keeping the strict instruction of no text in mind. At the center of the dotted line, a short arrow points towards each charge, depicting the force between them, coloured differently to stand out from the rest of the diagram. Overall, the illustration exudes an educational and comprehensible vibe.

Two equal charges are separated by 3.7 x 10^-10 m. The force between the charges has a magnitude of 2.37 x 10^-3 N. What is the magnitude of q on the charges?

can some one explain to me how to do this step by step. Not that great at math hope you can help. Thanks

There is a formula for the force (F) between two charges (Q1 and Q2), separated by a distance R. It is called Coulomb's Law. It must be in your text or notes; otherwise they would not have assigned this problem.

The formula says

F = k Q1*Q2/R^2

where k is a constant that equals 8.99*10^9 N*m^2/C^2

In your case, Q1 = Q2 = q, so

F = k*q^2/R^2

Rearrange the equation algebraically and solve for q

q = R sqrt(F/k)= 3.7*10^-10m*sqrt(2.636*10^-13)M/m
= 1.9*10^-16 Coulombs

Thanks!

q = R sqrt(F/k)

= 3.7*10^-10m*sqrt(2.636*10^-13)C/m
C stands for Coulombs
I typed M where it should be C

Well, it seems we have a shocking situation here! To solve for the magnitude of q on the charges, we can use Coulomb's Law. Coulomb's Law 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 break this down step by step:

Step 1: Write down the given information:
- Distance between the charges, r = 3.7 x 10^-10 m
- Force between the charges, F = 2.37 x 10^-3 N

Step 2: Recall the equation for Coulomb's Law, which is F = (k * q₁ * q₂) / r²

Step 3: We know that the charges are equal, so let's assume they have the same magnitude, q. Therefore, we can rewrite the equation as F = (k * q * q) / r²

Step 4: Rearrange the equation to solve for q:
(q * q) = (F * r²) / k
q = √((F * r²) / k)

Step 5: Plug in the given values:
- F = 2.37 x 10^-3 N
- r = 3.7 x 10^-10 m
- k is Coulomb's constant, which is approximately 9 x 10^9 N·m²/C²

Step 6: Time for some number crunching! Calculate:
q = √((2.37 x 10^-3 N * (3.7 x 10^-10 m)²) / (9 x 10^9 N·m²/C²))

After plugging in all these values and doing the calculations, you'll find the magnitude of q on the charges.

But hey, remember, even though math can be a bit shocking sometimes, it's always good to give it a try!

To find the magnitude of q on the charges, we can use Coulomb's Law, which states that the force between two charges is given by:

F = k * (|q1| * |q2|) / r^2

Where:
- F is the force between the charges
- k is Coulomb's constant, approximately equal to 9 x 10^9 Nm^2/C^2
- |q1| and |q2| are the magnitudes of the charges
- r is the distance between the charges

In this case, we are given the force (F) and the distance (r), and we need to find the magnitude of q on the charges.

Step 1: Identify the given information:
- F = 2.37 x 10^-3 N (force between the charges)
- r = 3.7 x 10^-10 m (distance between the charges)
- k = 9 x 10^9 Nm^2/C^2 (Coulomb's constant)

Step 2: Rearrange the equation to solve for |q1| * |q2|:
- Multiply both sides of Coulomb's Law by r^2: F * r^2 = k * (|q1| * |q2|)
- Divide both sides by k: (F * r^2) / k = |q1| * |q2|

Step 3: Substitute the given values into the equation:
(|q1| * |q2|) = (2.37 x 10^-3 N * (3.7 x 10^-10 m)^2) / (9 x 10^9 Nm^2/C^2)

Now we can calculate the value using a calculator:

(|q1| * |q2|) = (2.37 x 10^-3 N * (3.7 x 10^-10 m)^2) / (9 x 10^9 Nm^2/C^2)

= (2.37 x 10^-3 N * 1.369 x 10^-19 m^2) / (9 x 10^9 Nm^2/C^2)

= (3.25053 x 10^-22 Nm^2) / (9 x 10^9 Nm^2/C^2)

= 3.61 x 10^-32 C^2

Step 4: Take the square root of the value we obtained to find the magnitude of q on the charges:

|q| = √(3.61 x 10^-32 C^2)

|q| = 1.9 x 10^-16 C

Therefore, the magnitude of q on the charges is approximately 1.9 x 10^-16 C.