4. Find the magnitude of the force between two charges Q1 = 3µC, Q2 = 2.5µC that are 50mm apart.

What have you tried?

A quick search of force between two charges gives you Coulomb's Law:
F=(k*Q1*Q2)/d^2
Make sure your charges are in Coulombs and d is in metres.

To find the magnitude of the force between two 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.

The formula for Coulomb's law is:

F = (k * Q1 * Q2) / r^2

Where:
F is the magnitude of the force between the charges
k is the electrostatic constant (k = 8.99 * 10^9 N m^2/C^2)
Q1 and Q2 are the magnitudes of the charges
r is the distance between the charges

Given:
Q1 = 3µC = 3 * 10^-6 C
Q2 = 2.5µC = 2.5 * 10^-6 C
r = 50mm = 50 * 10^-3 m

Substituting the values into the formula, we get:

F = (8.99 * 10^9 N m^2/C^2 * (3 * 10^-6 C) * (2.5 * 10^-6 C)) / (50 * 10^-3 m)^2

Simplifying the expression, we have:

F = (8.99 * 10^9 N m^2/C^2 * 7.5 * 10^-12 C^2) / (2.5 * 10^-2 m)^2

F = (8.99 * 7.5 * 10^-3) / (2.5 * 10^-2)^2

F = 6.7425 * 10^-3 / 6.25 * 10^-4

F = 10.788 N

Therefore, the magnitude of the force between the two charges, Q1 = 3µC and Q2 = 2.5µC, that are 50mm apart is 10.788 N.

To calculate the magnitude of the force between two charges, we can use Coulomb's law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

The formula for Coulomb's law is:

F = (k * |Q1 * Q2|) / r^2

Where:
- F is the magnitude of the force between the charges,
- k is the electrostatic constant (k = 8.99 x 10^9 N·m^2/C^2),
- Q1 and Q2 are the charges of the two particles, and
- r is the distance between the charges.

In this case, we have Q1 = 3µC, Q2 = 2.5µC, and r = 50mm.

However, Coulomb's law requires the charges to be in SI units (Coulombs). Therefore, we need to convert the charges from microcoulombs (µC) to coulombs (C).

1 µC = 1 x 10^-6 C

So, Q1 = 3µC = 3 x 10^-6 C
And, Q2 = 2.5µC = 2.5 x 10^-6 C

Now, we can substitute these values into Coulomb's law:

F = (8.99 x 10^9 N·m^2/C^2) * |(3 x 10^-6 C) * (2.5 x 10^-6 C)| / (0.05 m)^2

F = (8.99 x 10^9 N·m^2/C^2) * (7.5 x 10^-12 C^2) / (0.05 m)^2

F = (8.99 x 10^9 N·m^2/C^2) * (7.5 x 10^-12 C^2) / (0.05^2 m^2)

F = (8.99 x 10^9 N·m^2/C^2) * (7.5 x 10^-12 C^2) / 0.0025 m^2

F = (8.99 x 10^9 N·m^2/(C^2 · m^2)) * (7.5 x 10^-12 C^2)

Calculating this expression, we can find the magnitude of the force between the two charges.