How Far Does a Charged Particle Travel Before Stopping?

In summary, the given problem involves a fixed charge of -4.00 x 10-6 C and a moving charge of -3.00 x 10-6 C, initially at a distance of 55.0cm with a speed of 15.0m/s, and the question asks for the distance the moving charge travels before stopping and returning. The equations used are V = k(Q/r), PE = (QV)/2, and KE = (mv2)/2. The correct formula for PE should be used instead of the energy stored in a capacitor, and the PE at point C should be compared with the PE at point B.
  • #1
lee_chick
3
0
Sorry for the poor title - I'm not entirely sure how to describe the type of problem!

Homework Statement



A charge of -4.00 x 10-6 C is fixed in place. From a horizontal distance of 55.0cm a particle of mass 2.50 x 10-3 kg and charge -3.00 x 10-6 C is fired with an initial speed of 15.0m/s directly towards the fixed charge. How far does the particle travel before it stops and begins to return back?

Homework Equations



V = k(Q/r)

PE = (QV)/2

KE = (mv2)/2

The Attempt at a Solution



I've tried this a few times and haven't found anything that works so here is my latest attempt:

A__________________________B_______________________C
A = fixed charge
B = unknown distance
C = Starting point for moving charge

Qa = -4.00 x 10-6 C
Qc = -3.00 x 10-6 C
v0c = 15m/s
v1c = 0m/s
mc = 2.50 x 10-3 kg
rc = 0.55m
rb = ?

rb = k(Qa/Vc)
Vc = 2PE/Qc
PE = -KE
KE = (mv2)/2

KE = (2.50 x 10-3 kg x -15m/s)/2 = -0.009375
PE = 0.009375

Vc = 2(0.009375)/-3.00 x 10-6 C = -6.25 x 103

rb = 9 x 109 (-4.00 x 10-6 C/-6.25 x 103) = 5.76 m
 
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  • #2
KE = 1/2*m*V^2
PE = k*Qa*Qc/rb
In this problem ra is not needed.
 
  • #3
lee_chick said:

Homework Equations



V = k(Q/r)

PE = (QV)/2
Don't confuse the PE between two point charges with the energy stored in a capacitor. Look up the correct formula for PE.

KE = (mv2)/2
Good.

Hint: Compare the PE at point C with the PE at point B.
 
  • #4
Thanks - I knew I was doing something wrong and just couldn't seem to sort out the problem correctly!
 

FAQ: How Far Does a Charged Particle Travel Before Stopping?

1. Where can I find the location of a point charge?

The location of a point charge can be determined by using a coordinate system, such as Cartesian or spherical coordinates, and specifying the distance and direction from a reference point.

2. How does the distance of a point charge affect its electric field?

The electric field of a point charge decreases with distance according to the inverse square law, meaning that as the distance increases, the electric field strength decreases.

3. Can a point charge have a negative location?

No, the location of a point charge is typically described as a distance and direction from a reference point, so it cannot be negative. However, the charge itself can be negative or positive.

4. How can the location of a point charge affect its potential energy?

The potential energy of a point charge depends on its location and the location of other charges in the system. The closer a point charge is to other charges, the higher the potential energy will be.

5. Is there a limit to how far a point charge can be located from other charges?

No, there is no limit to how far a point charge can be located from other charges. However, as the distance increases, the effect of the point charge on other charges will decrease due to the inverse square law.

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