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7. Consider a vacuum region, 0 < x < a, bounded by two grounded perfectly conducting walls at x = 0 and x = a. A surface charge density $\rho_0 \sin(\frac{3\pi}{a}x)$ is placed on y = 0, 0 < x < a. a) What is the electrostatic potential in the region 0 < x < a?(10%) b) What is the total charge (per unit length in z) on the surface of the conductor at x = 0? (10%)

Name: 7 consider a vacuum region 0 x a bounded by two grounded perfectly conducting walls at x 0 and x a a surface charge density rho0 sinfrac3piax is placed on y 0 0 x a a what is the electrosta 34022
Uploaded: 2024-07-30T03:40:42-08:00
Duration: 2 min 40 s
Channel: Adi S
Description: 7 consider a vacuum region 0 x a bounded by two grounded perfectly conducting walls at x 0 and x a a surface charge density rho0 sinfrac3piax is placed on y 0 0 x a a what is the electrosta 34022

          7. Consider a vacuum region, 0 < x < a, bounded by two grounded perfectly
conducting walls at x = 0 and x = a. A surface charge density $\rho_0 \sin(\frac{3\pi}{a}x)$ is
placed on y = 0, 0 < x < a.
a) What is the electrostatic potential in the region 0 < x < a?(10%)
b) What is the total charge (per unit length in z) on the surface of the conductor
at x = 0? (10%)

$7 consider a vacuum region 0 x a bounded by two grounded perfectly conducting walls at x 0 and x a a surface charge density rho0 sinfrac3piax is placed on y 0 0 x a a what is the electrosta 34022$

Added by John R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

07/30/2024

Step 1

$V(0) = 0 \implies C_2 = 0$ $V(a) = 0 \implies \frac{\rho_0 a^2}{9\pi^2\epsilon_0}\sin(3\pi) + C_1a = 0 \implies C_1 = 0$ Therefore, the electrostatic potential is: $V(x) = \frac{\rho_0 a^2}{9\pi^2\epsilon_0}\sin(\frac{3\pi}{a}x)$ Show more…

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7. Consider a vacuum region, 0 < x < a, bounded by two grounded perfectly conducting walls at x = 0 and x = a. A surface charge density $\rho_0 \sin(\frac{3\pi}{a}x)$ is placed on y = 0, 0 < x < a. a) What is the electrostatic potential in the region 0 < x < a?(10%) b) What is the total charge (per unit length in z) on the surface of the conductor at x = 0? (10%)