Question

Two small charged spheres, A and B, are separated by a distance of 0.50 meter. The charge on sphere A is +2.4 X 10^-6 coulomb and the charge on sphere B is --2.4 x 10^-6 coulomb
Calculate the magnitude of the electrostatic force that sphere A exerts on sphere B.

Answer 1

To calculate the magnitude of the electrostatic force that sphere A exerts on sphere B, we can use Coulomb's Law, which is given by the formula:

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

where:
- \( F \) is the magnitude of the force between the charges,
- \( k \) is Coulomb's constant, approximately \( 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2 \),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges, and
- \( r \) is the distance between the charges.

Substituting the values from the problem:
- \( q_1 = 2.4 \times 10^{-6} \, \text{C} \) (charge on sphere A),
- \( q_2 = 2.4 \times 10^{-6} \, \text{C} \) (charge on sphere B),
- \( r = 0.50 \, \text{m} \).

Now, substituting these values into the formula:

\[
F = 8.99 \times 10^9 \frac{|(2.4 \times 10^{-6}) \cdot (-2.4 \times 10^{-6})|}{(0.50)^2}
\]

Calculating the values in the formula step by step:

\[
|q_1 \cdot q_2| = |(2.4 \times 10^{-6}) \cdot (-2.4 \times 10^{-6})| = 2.4 \times 10^{-6} \cdot 2.4 \times 10^{-6} = 5.76 \times 10^{-12} \, \text{C}^2
\]

\[
r^2 = (0.50)^2 = 0.25 \, \text{m}^2
\]

Now substituting these into the force equation:

\[
F = 8.99 \times 10^9 \frac{5.76 \times 10^{-12}}{0.25}
\]

Calculating the fraction:

\[
\frac{5.76 \times 10^{-12}}{0.25} = 2.304 \times 10^{-11}
\]

So now substitute this back into the formula for \( F \):

\[
F = 8.99 \times 10^9 \cdot 2.304 \times 10^{-11}
\]

Now, calculating this product:

\[
F \approx 207.78 \, \text{N}
\]

Thus, the magnitude of the electrostatic force that sphere A exerts on sphere B is approximately:

\[
F \approx 207.8 \, \text{N}
\]