Hi, I'm currently doing a practice problem and I need help in solving it.(adsbygoogle = window.adsbygoogle || []).push({});

Ok first the problem:

a)Ok, the potential energy of the electron is: An insulated sphere of radiusRis charged unformly with the total charge+Q. Since the electric field is outwards, an electron of charge-e(insulated, so that it won't dissapear while traveling iside the charged sphere) placed at the surface will be pull toward the center of the sphere.

- What is the initial potential energy of the electron (relative to a point at infinity in terms of
QandR)?- Calculate the velocity of the electron (also in terms of
QandR) when it reaches the center of the sphere. Note that the electric field and hence the acceleration is not constant. Use the concept of conservation of kinetic and potential energies. Some simple integration is necessary to compute the potential at the center of the sphere.

[tex]U = -eV_R[/tex]

To find V of R we need to refer to electric field:

[tex]V_f - V_i = -\int_{i}^{f} \vec{E} \cdot d\vec{R}[/tex]

[tex]V(R) - V(\infty) = -\frac{Q}{4\pi\varepsilon_\varnothing} \int_{R}^{\infty} \frac{dR}{R}[/tex]

...

[tex]V_R = \frac{1}{4\pi\varepsilon_\varnothing}\frac{Q}{R}[/tex]

Therefore,

[tex]U = -eV_R[/tex]

[tex]U = \frac{1}{4\pi\varepsilon_\varnothing}\frac{-eQ}{R}[/tex]

B)This is the one I'm having trouble with. I don't know what the final potential energy is or out to get it.

Here's what I have so far:

[tex]U_\varnothing = K_f + U_f[/tex]

[tex]\frac{1}{4\pi\varepsilon_\varnothing}\frac{-eQ}{R} = \frac{1}{2}mv^2 + U_f[/tex]

So what do I do for U of f?

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# Homework Help: Electric Potential and Kinematics

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