Final answer:
To find the closest distance the particle gets to the fixed charge before coming to rest, we use energy conservation by equating the particle's initial kinetic energy with the electric potential energy at the point of closest approach. Using the masses and charges provided, we can solve for the distance r where the speed of the particle becomes zero.
Step-by-step explanation:
To determine how close the particle with a charge of +3.40 μC and mass 5.20 g gets to the fixed charge of 4.50 μC before it comes to rest, we use the conservation of energy. The particle's initial kinetic energy is converted into electric potential energy as it approaches the fixed charge, at which point it comes to rest momentarily before being pushed away by the electrostatic force.
The initial kinetic energy (½mv²) of the particle is given by:
- Mass (m): 5.20 g = 0.00520 kg
- Initial speed (v): 60.0 m/s
Kinetic Energy (KE) = ½ * 0.00520 kg * (60.0 m/s)²
The electrostatic potential energy (U) at a distance (r) between two point charges (q1 and q2) is given by:
U = k * q1 * q2 / r
Here, k is Coulomb's constant (8.9875517873681764 × 10⁹ N·m²/C²).
Setting the kinetic energy equal to the potential energy and solving for r yields the closest distance before the particle comes to rest.
Therefore, to find the distance r, we use:
KE = U
½mv² = k * q1 * q2 / r
Solving for r allows us to find the minimum distance at which the particle's speed becomes zero before being repelled back.
This is a physics problem that involves principles from the topic of electrostatics and the application of energy conservation.