Volume Element.pdf | Lecture Note - Edubirdie

University:
Santa Fe College
Course:
PHY 2048 | General Physics 1 with Calculus
Academic year:

2024
Views:

338

Pages:

4
Author:

Jabin F.

Volume element.- The text introduces variables 'de', 'r', 'd(lo)', 'd(lo)', 'p', 'R', and 'T', and presents equations involving them. The equations involve integrals and trigonometric functions. The handwriting is neat and legible. Hemisphere of Radius R is placed in Uniform Electric field Eoz Calculate the E-flux crossing through Hemispherical surface /phinet = /phioisc + /phispherical = 0 /phidisc = ∫∫Ex2molrdφdr 0 0 /phiDisc =-EAR² 2 Spherical = Dues. in A sphere of Radius R is placed an Electric field E= +(28+ βsines$$). Colaulated het flux associated with the sphor Psphoriat Sends = S(OE) de = = \[=\alpha R\int_{0}\int_{0}^{1}sin\theta d\theta d\phi\] \[\begin{matrix}\hat{\phi}\cdot\hat{r}=0\\ \hat{\gamma}\cdot\hat{r}=\phi\end{matrix}\] A non-Conducting thin ellipsoidal cell defined by the ept (x^{2}+2y^{2}+3z^{2}=a^{2}) as a net charge & spreads Uniform over it surface. The flux passing through. hemispherical surface defined by- (x^{2}+y^{2}+z^{2}=a^{2}) and 270 → Solh [x^{2}+2y^{2}+3z^{2}=a^{2}] [\frac{x^{2}}{a^{2}}+\frac{y^{2}}{(\frac{a}{\sqrt{2}})^{2}}+\frac{z}{(\frac{a}{\sqrt{3}})^{2}}=1] 1 This hemisphose enloses halfof ellipsoid Completely. [x^{2}+y^{2}+z^{2}=a^{2}] [\frac{x^{2}}{a^{2}}+\frac{y^{2}}{a^{2}}+\frac{z^{2}}{a^{2}}=1] [\phi_{E}=\oint_{S}\vec{\epsilon}.d\vec{s}=\frac{q}{\epsilon_{o}}] [\Phi_{E}(sphere)=\frac{\phi}{\epsilon_{0}}] Ques.24 The charge density as a f" of radial distancer is given by - ρ(r) = ρo (R²/r²) for r≤R = 0 for r>R Electric flux over the surface of ellipsoid with anpils BR, 4R & 5R centred at the origin (Chargedensity only in sphore) There are multiple lines of equations, including integrals, variables, and numerical values. The overall structure appears to be a step-by-step calculation or derivation.

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