A charge of +2 X 10^-7 C is 10 cm from a charge of -6 X 10^-6 C. Find the magnitude and direction of the force of each charge.
Could someone help me with this problem. I don't know what to do.
force= kQ1*Q2/distance^2 distance is .1m
Sure! I can help you solve this problem.
To find the magnitude and direction of the force between two 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 down the problem step by step:
Step 1: Identify the given values
The given values in the problem are:
- Charge 1 (q1) = +2 x 10^-7 C (in Coulombs)
- Charge 2 (q2) = -6 x 10^-6 C (in Coulombs)
- Distance between the charges (r) = 10 cm = 0.1 m
Step 2: Convert the charges to the same unit
Both charges are given in Coulombs, so we don't need to do any unit conversion in this case.
Step 3: Calculate the magnitude of the force
Using Coulomb's Law, the formula to calculate the magnitude of the force between two charges is:
F = (k * |q1 * q2|) / r^2
where:
- F is the magnitude of the force
- k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2)
- q1 and q2 are the magnitudes of the charges
- r is the distance between the charges
Plugging in the values we have:
F = (9 x 10^9 Nm^2/C^2 * |2 x 10^-7 C * (-6 x 10^-6 C)|) / (0.1 m)^2
F = (9 x 10^9 Nm^2/C^2 * (2 x 10^-7 C * 6 x 10^-6 C)) / 0.01 m^2
F = (9 x 10^9 Nm^2/C^2 * 12 x 10^-13 C^2) / 0.01 m^2
F = 108 x 10^-4 N
Therefore, the magnitude of the force between the charges is 108 x 10^-4 N.
Step 4: Determine the direction of the force
The direction of the force is determined by the nature of the charges. Charges with the same sign (either both positive or both negative) repel each other, while charges with opposite signs attract each other.
In this case, we have a positive charge (+) and a negative charge (-). Therefore, the force will be attractive. The force vector will point from the negative charge towards the positive charge.
To summarize:
- The magnitude of the force is 108 x 10^-4 N.
- The direction of the force is from the negative charge towards the positive charge.
I hope this explanation helps! Let me know if you have any further questions.