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cheyenneperuchi
31.08.2020 •
Physics
A solid sphere of radius R has a uniform charge density and total charge Q. Find the total energy of the sphere U in terms of
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Ответ:
Explanation:
From the information given;
The surface area of a sphere =![4 \pi r ^2](/tpl/images/0735/0259/14bb6.png)
If the sphere is from the collection of spherical shells of infinitesimal thickness = dr
Then,
the volume of the thickness and the sphere is;
V =![4 \pi r ^2 \ dr](/tpl/images/0735/0259/7b963.png)
Using Gauss Law
here,
q(r) =charge built up contained in radius r
since we are talking about collections of spherical shells, to work required for the next spherical shell r +dr is
where;
dq which is the charge contained in the next shell of charge
here dq = volume of the shell multiply by the density
equating it all together
Integration the work required from the initial radius r to the final radius R, we get;
Recall that:
the total charge on a sphere, i.e![Q_{total} = \dfrac{4}{3} \pi R^3 \rho](/tpl/images/0735/0259/498a8.png)
Then :
Ответ:
The work done was W=720lb.ft
Explanation:
Here weight is a lineal function of the vertical position. Let's put it in the following way:
where w is the weight and y is the vertical position (how high it is the bag).
So, from the information given:
∴![w(y)=-7.2\frac{lb}{ft}y+144lb](/tpl/images/0233/6015/e1099.png)
So, the work done will be:
∴ W=720lb.ft