Questions: What is the magnitude of the acceleration, a in m / s^2, experienced by charge Q2? a= m / s^2

Solution Steps

We need to find the magnitude of the acceleration \( a \) experienced by charge \( Q_2 \). To do this, we need to use the formula for the force between two charges and then apply Newton's second law.

Coulomb's Law gives the force between two point charges: \[ F = k_e \frac{|Q_1 Q_2|}{r^2} \] where:

• \( k_e \) is Coulomb's constant (\( 8.9875 \times 10^9 \, \mathrm{N \cdot m^2 / C^2} \)),
• \( Q_1 \) and \( Q_2 \) are the magnitudes of the charges,
• \( r \) is the distance between the charges.

Newton's second law states: \[ F = m a \] where:

• \( F \) is the force,
• \( m \) is the mass of the object,
• \( a \) is the acceleration.

To find the acceleration \( a \), we rearrange Newton's second law: \[ a = \frac{F}{m} \] Substituting the force from Coulomb's law: \[ a = \frac{k_e \frac{|Q_1 Q_2|}{r^2}}{m} \] Simplifying: \[ a = k_e \frac{|Q_1 Q_2|}{m r^2} \]

Assume we have the following values:

• \( Q_1 = 1 \, \mathrm{C} \)
• \( Q_2 = 1 \, \mathrm{C} \)
• \( r = 1 \, \mathrm{m} \)
• \( m = 1 \, \mathrm{kg} \)

Substitute these values into the equation: \[ a = 8.9875 \times 10^9 \frac{(1 \times 1)}{1 \times 1^2} \] \[ a = 8.9875 \times 10^9 \, \mathrm{m/s^2} \]

Final Answer