- #1
madafo3435
- 55
- 15
- Homework Statement
- A charge distribution with a uniform positive charge surface density + σ is formed by a circular section of radii R1 and R2.
- Relevant Equations
- Charges to continuous charge distributions
I would like if my procedure is correct ...
Due to the symmetry of the problem, I only worry about the vertical coordinate of the field, so I will work with the magnitude of the field, and I will treat the problem in polar coordinates.
Is this correct?
Due to the symmetry of the problem, I only worry about the vertical coordinate of the field, so I will work with the magnitude of the field, and I will treat the problem in polar coordinates.
##E= \int_{R_1} ^ {R_2} \int_{0} ^ {\pi} \frac {\sigma sen(\theta)}{4\pi \epsilon _0 r^2} rd\theta dr = \frac {\sigma}{4\pi \epsilon _0} \int_{R_1}^{R_2} \frac {2}{r} dr = \frac {\sigma}{2\pi \epsilon _0} ln(\frac {R_2}{R_1})##
## \therefore \vec{E} = \frac {\sigma}{2\pi \epsilon _0} ln(\frac {R_2}{R_1}) \hat{\jmath} ##
I attach a picture of the problem below.## \therefore \vec{E} = \frac {\sigma}{2\pi \epsilon _0} ln(\frac {R_2}{R_1}) \hat{\jmath} ##
Is this correct?