9. Homework Due on 23.08.2022: Consider a uniformly polarized sphere of radius $R$ such that $\vec{P} = P_0 \vec{k}$. Use $\sigma_p$ and $\rho_p$ and for a point $\vec{r} = z \vec{k}$ along the $z$ axis, to show that, $\psi_{outside} = \frac{P_0}{4 \pi \epsilon_0 z^2}$, $\vec{E}_{outside} = \frac{2p}{4 \pi \epsilon_0 z^3} \vec{k}$, $p = \frac{4}{3} \pi R^3 P_0$ $\psi_{inside} = \frac{P_0 z}{3 \epsilon_0}$, $\vec{E}_{inside} = -\frac{P_0}{3 \epsilon_0} \vec{k}$. (14) (15)
Added by Alex G.
Close
Step 1
To find the electric field outside the sphere, we can use Gauss's law. Gauss's law states that the electric flux through a closed surface is equal to the charge enclosed divided by the permittivity of free space (Īµ0). Since the sphere is uniformly polarized, the Show moreā¦
Show all steps
Your feedback will help us improve your experience
Krishna J and 99 other Physics 103 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let $S$ be the sphere of radius $R$ centered at the origin. Explain using symmetry: $$ \iint_{S} x^{2} d S=\iint_{S} y^{2} d S=\iint_{S} z^{2} d S $$ Then show that $\iint_{S} x^{2} d S=\frac{4}{3} \pi R^{4}$ by adding the integrals.
LINE AND SURFACE INTEGRALS
Parametrized Surfaces and Surface Integrals
Use spherical coordinates. Evaluate xyz dV, where E lies between the spheres p = 3 and p = 7 and above the cone phi = pi/3. 14615/8 pi
William S.
Theorem 4.11: On a sphere of radius R = 1, the area of the spherical polygonal region P formed by n-gon A1A2...An with vertex angles Ģ1, Ģ2, ..., Ģn, where each Ģi < Ģ, is given by Area(P) = (āĢi) - (n - 2)Ģ.
Sri K.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD