Potential Energy Question

[computerages]

Hello, everyone,

 

Following is the question that I am not really able to do. I would be grateful if someone can guide me through the solution.

 

Thanks

 

The electric-field strength as a function of position x in a certain region is given by [math]E = E_0 \left( {x/x_0 } \right)[/math], where [math]E0 = 26 {\rm kV/m}[/math] and [math]x_{0} = 5.2 {\rm m}[/math]. Find the total energy stored in a cube [math]1.0 {\rm m}[/math] on a side located between [math]x = 0[/math] and [math]x = 1.0\;{\rm{ m}}[/math]. Note: The field strength is independent of y and z.

[swansont]

How does potential energy relate to the electric field?

[computerages]

Hi,

 

I derived this equation U=Eqr from V=U/q, and E=kq/r^2. But q is not given in the problem, where do I go from here?

 

edit:

 

I used the equation [math]U={1/2}{\varepsilon_{0}} \int E^{2}dV[/math] and E.F. equation given in the question to solve for U. After simplifying, I needed to compute the integral [math]\int_0^1 x^{2} dV[/math]. At first, I tried to have [math]dV[/math] in terms of [math]x[/math], but the answer was incorrect. Then I took the integral with respect to [math]x[/math] ignoring [math]dV[/math]. but I got the correct answer.

 

Can anyone explain why I was able to compute the integral of [math]x^{2}[/math] without respect to [math]x[/math]...

 

Thanks

 

Can anyone answer my question, please.

 

thanks