- #1

agnimusayoti

- 240

- 23

- Homework Statement
- Use Eq 2.29 to calculate potential inside a uniformly charged solid sphere of radius R and total charge q. Compare tour answer to Prob 2.21

- Relevant Equations
- Eq. 2.29:

$$V(\vec r)=\frac{1}{4 \pi \epsilon_0} \int \frac{\rho (\vec r')}{\mu} d\tau' $$

where ##\mu## is distance from ##d\tau'##

Well, in this problem, I try to use

$$d \tau '= \mu ^2 \sin {\theta} {d\mu} {d\theta} {d\phi}$$

With these domain integration:

$$0<\mu<r$$

$$0<\theta<\pi$$

$$0<\phi<2\pi$$

, I get $$V=\frac{1}{4\pi \epsilon_0} \frac{3Qr^2}{2R^3}$$

This result is wrong because doesn't match with Prob 2.21, which potential is determined with line integral.

I suspect that I made a mistake when define the ##\mu##, which is distance from volume element to point of analysis. Could you please what is wrong and how to fix it? Thanks

$$d \tau '= \mu ^2 \sin {\theta} {d\mu} {d\theta} {d\phi}$$

With these domain integration:

$$0<\mu<r$$

$$0<\theta<\pi$$

$$0<\phi<2\pi$$

, I get $$V=\frac{1}{4\pi \epsilon_0} \frac{3Qr^2}{2R^3}$$

This result is wrong because doesn't match with Prob 2.21, which potential is determined with line integral.

I suspect that I made a mistake when define the ##\mu##, which is distance from volume element to point of analysis. Could you please what is wrong and how to fix it? Thanks