Charge Q = 6.00 microcoulombs is distributed uniformly over the volume of an insulating sphere...

Question:

Charge Q = 6.00 {eq}\displaystyle \mu C {/eq} is distributed uniformly over the volume of an insulating sphere that has radius R = 14.0 cm.

A small sphere with charge q = +3.00 {eq}\displaystyle \mu C {/eq} and mass {eq}\displaystyle 6.00 \ X \ 10^{-5} {/eq} kg is projected toward the center of the large sphere from an initial large distance.

The large sphere is held at a fixed position and the small sphere can be treated as a point charge.

What minimum speed must the small sphere have in order to come within 6.00 cm of the surface of the large sphere?

Energy conservation

We know that from the law of energy conservation that energy can neither be created nor be destroyed it can only change its forms from one to another. Therefore, the total energy of the system would remain constant at every instant.

Answer and Explanation:

Let us consider that the velocity of the charge q is "V" initially,

therefore the initial kinetic energy of the charge would be

{eq}\displaystyle E = 0.5mV^{2} \\ E = 0.5*6*10^{-5}V^{2} \\ E = 3*10^{-5}V^{2} \ J {/eq}

Now when this charge reaches the near to the charge Q, then its kinetic energy will get converted into the potential energy,

therefore the final energy would be

{eq}\displaystyle E_{f} = \dfrac{kqQ}{r} \\ E_{f} = \dfrac{9*10^{9}*6*10^{-6}*3*10^{-6}}{(0.13)^{2}} \\ E_{f} = 9.586 \ J {/eq}

Now, applying the energy conservation

{eq}\displaystyle E = E_{f} \\ 3*10^{-5}V^{2} = 9.586 \\ V = 565.267 \ m/s {/eq}


Learn more about this topic:

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Energy Conservation and Energy Efficiency: Examples and Differences

from Geography 101: Human & Cultural Geography

Chapter 13 / Lesson 9
100K

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