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hey,

i have a question from an exam paper which isn't worded too nicely (most of the questions on the exam are worded in similar ways :grumpy:)

The way i've done it is to first put in my first

[tex]U = \frac{n dq^{2}}{4 \pi \epsilon _{0} R}[/tex]

where

so the total Electrostatic energy of the whole thing (with all the shells assembled) is going to be:

[tex]U=\Sigma^{n}_{i=1} \frac{i dq^{2}}{4 \pi \epsilon_{0} R}[/tex] Where [tex]n dq = Q[/tex]

I can turn that into an integral (Replacing one of the

[tex]U = \int ^{Q}_{0} \frac{q dq}{4 \pi \epsilon_{0} R} dq[/tex]

This goes to [tex]U=\frac{Q^{2}}{8 \pi \epsilon_{0} R}[/tex]

now i make it so it's shells rather than points;

[tex]U=\int^{2\pi}_{0}\int^{\pi}_{0}\frac{Q^{2}}{8 \pi \epsilon_{0} R} d\theta d\varphi[/tex]

[tex]U=\frac{\pi Q^{2}}{4 \epsilon_0 R}[/tex]

Could someone confirm whether or not this is correct please?

i have a question from an exam paper which isn't worded too nicely (most of the questions on the exam are worded in similar ways :grumpy:)

Determine the electrostatic energyUof a thin spherical shell of radiusRwhich carries chareQuniformly distributed over it's surface [Hint: imagine to assemble the sperical shell by superimposing sheels of radius R and infintesimal chargedq. ].

The way i've done it is to first put in my first

*shell of infintesimal charge*and then treat it as a point charge. Then i treat the next shell as just a point, and place it at a distance*R*from the point (electrostatic energy of this;[tex]U = \frac{n dq^{2}}{4 \pi \epsilon _{0} R}[/tex]

where

*n*is the number of shells already added.so the total Electrostatic energy of the whole thing (with all the shells assembled) is going to be:

[tex]U=\Sigma^{n}_{i=1} \frac{i dq^{2}}{4 \pi \epsilon_{0} R}[/tex] Where [tex]n dq = Q[/tex]

I can turn that into an integral (Replacing one of the

*dq*s with [tex]\frac{q}{dq}[/tex]) ;[tex]U = \int ^{Q}_{0} \frac{q dq}{4 \pi \epsilon_{0} R} dq[/tex]

This goes to [tex]U=\frac{Q^{2}}{8 \pi \epsilon_{0} R}[/tex]

now i make it so it's shells rather than points;

[tex]U=\int^{2\pi}_{0}\int^{\pi}_{0}\frac{Q^{2}}{8 \pi \epsilon_{0} R} d\theta d\varphi[/tex]

[tex]U=\frac{\pi Q^{2}}{4 \epsilon_0 R}[/tex]

Could someone confirm whether or not this is correct please?

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