University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

235

Pages:

5
Author:

Jabin F.

Current Inside The Wire [\vec{J} = J_{z}\hat{z}] [\mathcal{I}{enc.} = \iint{S}\vec{J}d\vec{s}_{l}] [\mathcal{I}{enc.} = \int{0}^{2\pi}\int_{0}^{a}J_{0}(\frac{\alpha^{2}-\gamma^{2}}{a^{2}})\gamma d\gamma d\phi] [\mathcal{I}{enc.} = 2\pi J{0}(\frac{a^{2}}{2}-\frac{a^{4}}{4a^{2}})] [\mathcal{I}{enc.} = 2\pi J{0}(\frac{a^{2}}{2}-\frac{a^{2}}{4})] [\mathcal{I}{enc.} = 2\pi J{0}(\frac{a^{2}}{4})] [\oint\vec{B}d\vec{l} = \mu_{0}\mathcal{I}_{enc.}] [\vec{B}(2\pi r) = \mu_{0} \cdot 2\pi J_{0}(\frac{a^{2}}{4})] [\vec{B}{in} = \mu{0}J_{0}(\frac{r}{2}-\frac{r^{3}}{4a^{2}})\hat{\phi}] [J_{in} \propto (y_{0} - y^{2})] [B_{in} \propto (r^{2} - r^{3})] or [B_{out} \propto \frac{1}{r}] Q. No. 33 Page-63 [\vec{B}{in} = \mu{0}n\hat{z}] [\vec{B}_{out} = 0] # Induced electric field Outside [\oint\vec{E}{out}d\vec{l} = -\int{S}\frac{\partial\vec{B}}{\partial t}d\vec{S}] [\vec{E}.2\pi r = -\mu_{0}n\pi R^{2}\frac{\partial I}{\partial t}] [\vec{E}{out} = \frac{-\mu{0}nR^{2}}{2\pi r}\frac{\partial I}{\partial t}\hat{\phi}]