What is the magnitude of the force a +23 µC charge exerts on a +3.5 mC charge 49 cm away?

A 1 μC charge is 5 cm away from a -2 μC charge. What is the magnitude and direction of the force on the 1 μC charge?

To calculate the magnitude of the force between two charges, we can use Coulomb's Law:

\[F = k \times \frac{{|q_1 \cdot q_2|}}{{r^2}}\]

Where:
F is the magnitude of the force between the charges (in Newtons),
k is the electrostatic constant (\(9 \times 10^9 \, \text{Nm}^2/\text{C}^2\)),
\(q_1\) and \(q_2\) are the magnitudes of the charges (in Coulombs), and
r is the distance between the charges (in meters).

Given:
\(q_1 = +23 \, \mu \text{C} = +23 \times 10^{-6} \, \text{C}\),
\(q_2 = +3.5 \, \text{mC} = +3.5 \times 10^{-3} \, \text{C}\), and
\(r = 49 \, \text{cm} = 49 \times 10^{-2} \, \text{m}\).

Substituting these values into the equation:

\[F = (9 \times 10^9 \, \text{Nm}^2/\text{C}^2) \times \frac{{|(23 \times 10^{-6}\, \text{C}) \cdot (3.5 \times 10^{-3}\, \text{C}) |}}{{(49 \times 10^{-2} \, \text{m})^2}}\]

Calculating this expression gives us the magnitude of the force between the charges.

To find the magnitude of the force between two charges, we can use Coulomb's law formula:

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

Where:
- F is the magnitude of the force
- k is the electrostatic constant, approximately equal to 8.99 x 10^9 N m^2/C^2
- q1 and q2 are the magnitudes of the two charges
- r is the distance between the charges

In this case:
- q1 = +23 µC = +23 * 10^(-6) C
- q2 = +3.5 mC = +3.5 * 10^(-3) C
- r = 49 cm = 49 * 10^(-2) m

Substituting these values into the formula:

F = (k * |q1 * q2|) / r^2
= (8.99 x 10^9 N m^2/C^2) * (|+23 * 10^(-6) C * +3.5 * 10^(-3) C|) / (49 * 10^(-2) m)^2

Now we can calculate the magnitude of the force.