Electric potential and kinetic energy

In summary, the minimum distance between the two objects when Q=1.0 μC, q=1.0 nC, m=1.0*105 kg, and v= 3.0*105m/s is 2*10^-11 meters. This problem is similar to the escape velocity problem in terms of the final distance being irrelevant as long as it is large. The initial starting position can be disregarded in the calculation.
  • #1
tony873004
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Homework Statement


A point charge Q is fixed in position, and a second object with charge q and mass m moves directly toward it from a great distance. If the initial speed of the object is v, compute the minimum distance between the two objects. If Q=1.0 μC, q=1.0 nC, m=1.0*105 kg, and v= 3.0*105m/s, what is the minimum distance of approach?


Homework Equations





The Attempt at a Solution



[tex]\begin{array}{l}
\frac{{kQq}}{{r_1 }} + \frac{1}{2}mv_0^2 = \frac{{kQq}}{{r_2 }} + \frac{1}{2}v_f^2 ,\,\,\,\,\,\,\,\,\,\,\,\,v_f = 0 \\
\\
\frac{{kQq}}{{r_1 }} + \frac{1}{2}mv_0^2 = \frac{{kQq}}{{r_2 }} \\
\\
r_2 = \frac{{kQq}}{{\left( {\frac{{kQq}}{{r_1 }} + \frac{1}{2}mv_0^2 } \right)}} \\
\\
r_2 = \frac{{8.99 \times 10^9 {\rm{N}} \cdot \frac{{{\rm{m}}^{\rm{2}} }}{{{\rm{C}}^{\rm{2}} }}1.0\mu {\rm{C}} \cdot 1.0{\rm{nC}}}}{{\left( {\frac{{8.99 \times 10^9 {\rm{N}} \cdot \frac{{{\rm{m}}^{\rm{2}} }}{{{\rm{C}}^{\rm{2}} }}1.0\mu {\rm{C}} \cdot 1.0{\rm{nC}}}}{{r_1 }} + \frac{1}{2}1.0 \times 10^{ - 5} \cdot 3.0 \times 10^5 } \right)}} \\
\end{array}[/tex]

This reminds me somewhat of gravity's escape velocity problem, where your final distance is irrelevant as long as it is large (theoretically infinity).

How do I dismiss r1, the initial starting position in this problem? Can I just get rid of the entire first term in the denominator, since when r1 is large, it approaches 0?

Thanks!

**edit, 3*105 should be (3*105)2. I get 2*10-11 meters for the answer. Did I do this right?
 
Last edited:
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  • #2
Your answer is correct.
 
  • #3


I would like to commend you on your attempt at solving this problem using the appropriate equations and units. Your approach seems to be correct and your final answer of 2*10^-11 meters also seems reasonable.

To address your question about dismissing r1, in this case, it is not necessary to do so as it represents the initial starting distance between the two objects. As you correctly stated, when r1 is large, the first term in the denominator approaches 0, but it still needs to be included in the equation for accuracy.

Additionally, I would like to mention that the first term in the denominator represents the electric potential energy of the system, while the second term represents the kinetic energy of the moving object. As the object approaches the fixed charge, its kinetic energy is converted into electric potential energy, resulting in a decrease in its speed (v_f = 0). This is what allows us to solve for the minimum distance between the two objects.

Overall, your response shows a good understanding of electric potential and kinetic energy and how they relate to this problem. Keep up the good work!
 

Related to Electric potential and kinetic energy

1. What is electric potential energy?

Electric potential energy is the energy that an electric charge possesses by virtue of its position in an electric field. It is a form of potential energy that depends on the configuration of the electric charges in the field.

2. How is electric potential energy related to electric potential?

Electric potential energy and electric potential are closely related. Electric potential is the amount of electric potential energy per unit charge at a given point in an electric field. In other words, electric potential is a measure of the potential energy that a charge would have if placed at that point in the field.

3. What is the difference between electric potential and electric potential energy?

Electric potential is a measure of the potential energy per unit charge at a given point in an electric field, while electric potential energy is the total amount of potential energy that a charge possesses in an electric field. So, electric potential is a property of the field itself, while electric potential energy is a property of the charged particles within the field.

4. How does kinetic energy relate to electric potential and electric potential energy?

Kinetic energy is the energy that a moving object possesses by virtue of its motion. In the context of electric potential and electric potential energy, kinetic energy is related to the movement of charged particles in an electric field. As a charged particle moves in an electric field, it can gain or lose potential energy, which can then be converted into kinetic energy.

5. What is the formula for calculating electric potential energy?

The formula for calculating electric potential energy is U = qV, where U is the potential energy, q is the charge of the particle, and V is the electric potential at the location of the particle. This formula assumes a point charge in a uniform electric field. For more complex configurations, the formula may be more complex.

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