Accelerating Charges: Analyzing Test Charge Motion

[PhyDude]

Homework Statement

A positive test charge is brought near a stationery fixed point charge. The positive test charge is then released. How does the test charge move after it is released?
a) Constant Velocity
b) Increasing Acceleration
c) Decreasing Acceleration
d) Constant Acceleration

Homework Equations

The problem that I had with this question is that after the positive test charge is released, it obviously experiences a force and therefore acceleration but but how exactly is the answer justified. Sure you could use Coulombs law to determine the force but the problem is that Coulomb's Law can't be used because the particle is accelerating and because Coulomb's Law states that the Electrostatic force between two charges can only be determined as long as the charges are stationery or they are slow moving. When charges accelerate, the force that on charge exerts on another is not simply Coulomb's Law.

The Attempt at a Solution

 

[Fwahnak]

The question is not asking you to derive a trajectory for the test charge so the specific forces don't seem to be overly important. Yes moving charges create magnetic fields and radiate electomagnetic enegry but considering these things seems to be overcomplicating the question some what.

I think the heart of the problem is:
Is the force that the charges feel dependent on their relative distance?
You have 2 situations either the fixed charge is possitive or negative. How does the test charge move in these 2 cases?

 

[tomcue]

I would approach this problem by first considering the basic principles of electrostatics and Newton's laws of motion. The positive test charge experiences a force due to the fixed point charge, which is given by Coulomb's Law. However, as the test charge is released, it starts to accelerate due to this force. This acceleration can be determined by using Newton's second law, which states that the net force on an object is equal to its mass multiplied by its acceleration.

Therefore, the test charge will experience a constant acceleration as it moves towards the fixed point charge. This is because the force between the two charges remains constant and the mass of the test charge also remains constant. This can be represented by the equation F=ma, where F is the force between the two charges, m is the mass of the test charge, and a is its acceleration.

In conclusion, the correct answer to the question is d) Constant Acceleration. This is because the test charge will continue to accelerate towards the fixed point charge at a constant rate, as determined by Newton's second law, until it reaches a certain distance and the force between the two charges becomes negligible.