- #36
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I'm not sure if this makes any sense but for the potential to be zero at infinity, don't we need to integrate from infinity to the outer shell for the potential outside the outer shell (which would give 0)
then, to get the potential between R2>r>R1 we integrate from R2 to R1
using gauss law we can find the E-field in between the shells
[tex]E=\frac{kQ_1}{r^2}[/tex]
then the potential would be:
[tex] V=-k Q_1 \int_{R_2}^r \frac{1}{r^2} dr [/tex]
[tex] V = kQ_1 \left( \frac{1}{r} - \frac{1}{R_2} \right) [/tex]
then, to get the potential between R2>r>R1 we integrate from R2 to R1
using gauss law we can find the E-field in between the shells
[tex]E=\frac{kQ_1}{r^2}[/tex]
then the potential would be:
[tex] V=-k Q_1 \int_{R_2}^r \frac{1}{r^2} dr [/tex]
[tex] V = kQ_1 \left( \frac{1}{r} - \frac{1}{R_2} \right) [/tex]