How Far Does a Charged Particle Travel Before Stopping Due to Repulsive Force?

In summary, the problem involves a fixed charge of -3 microC and a particle with a mass of 7.2 x 10^-3 kg and charge of -8 microC, fired at a speed of 65 m/s towards the fixed charge from a horizontal distance of 0.045 m. The task is to determine the distance the particle will travel before its speed reaches zero. The solution involves using Coulomb's law and equations of motion, but the difficulty lies in the increasing repulsive force as the particle travels towards the fixed charge. However, the initial kinetic energy and the concept of work can be used to overcome this challenge. Therefore, the solution involves calculating the change in voltage needed to overcome the kinetic energy of the
  • #1
Nivlac2425
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Homework Statement


A charge of -3 microC is fixed in place. From a horizontal distance of 0.045m, a particle of mass 7.2 x 10^-3 kg and charge -8 microC is fired with an initial speed of 65 m/s directly toward the fixed charge. How far does the particle travel before its speed is zero?


Homework Equations


equations of motion
Coulomb's law, to possibly find repulsive force?


The Attempt at a Solution


I tried to use Colomb's law to find the repulsive force, then F=ma to find the deceleration. After that I used equations of motion to find the distance to reach 0m/s. this didn't work, and I think it is because the repulsive force increases as the particle travels towards the fixed change.

I am stuck at how to solve this problem at this point.
Thanks everyone in advance for helping! =)
 
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  • #2
The problem is that as it gets closer the field strength increases because of the decreasing distance.

But not to despair.

They give you the initial kinetic energy.

And you also know that W = q*ΔV

Figure then the change in voltage needed to overcome the kinetic energy of the particle?
 
  • #3


As you correctly noted, the repulsive force between the two charges will increase as the particle gets closer to the fixed charge. This means that the particle will experience a varying acceleration as it moves towards the fixed charge. To solve this problem, you will need to use calculus and the equation for Coulomb's law to calculate the acceleration at each point along the particle's path. Then, you can use the equations of motion to find the distance traveled before the particle's speed reaches zero. Alternatively, you could also use conservation of energy to solve for the distance traveled.
 

Related to How Far Does a Charged Particle Travel Before Stopping Due to Repulsive Force?

What is repulsive force of charges?

Repulsive force of charges refers to the force exerted between two charged particles that have the same type of charge (either both positive or both negative). This force causes the particles to push away from each other.

How is repulsive force of charges calculated?

The repulsive force of charges can be calculated using Coulomb's law, which states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

What factors affect the strength of repulsive force of charges?

The strength of repulsive force between two charged particles depends on the magnitude of their charges and the distance between them. The larger the charges and the closer the particles are, the stronger the repulsive force will be.

Can repulsive force of charges be observed in everyday life?

Yes, repulsive force of charges can be observed in many everyday situations. For example, when you rub a balloon on your hair, the balloon becomes charged and can repel other charged objects like your hair or a wall. This is due to the repulsive force between the charges on the balloon and the charges on the other objects.

Can repulsive force of charges be used for practical applications?

Yes, repulsive force of charges has various practical applications, such as in electrostatic precipitators used to remove pollutants from smokestacks, inkjet printers, and particle accelerators. It also plays a crucial role in the stability of everyday objects like atoms and molecules.

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