Question

1. Consider a solid ball of radius R centered at the origin carrying a charge density $\rho(r) = 1 + k\frac{r^2}{R^2}$ for $0 \le r \le R$, where k is a constant. (a) Using Gauss's law, find the electric field inside and outside the ball. (b) Find the electric potential inside and outside the ball, taking infinity as the reference point. (c) Calculate the work required to assemble this charge distribution in two different ways: i. Using $W = \frac{\epsilon_0}{2} \int_{\text{all space}} E^2 d\tau$. ii. Using $W = \frac{1}{2} \int_D \rho V d\tau$.

Name: 1 consider a solid ball of radius r centered at the origin carrying a charge density rhor 1 kfracr2r2 for 0 le r le r where k is a constant a using gausss law find the electric field inside 34601
Uploaded: 2019-08-10T22:59:56-08:00
Duration: 4 min 29 s
Channel: Bruce Edelman
Description: 1 consider a solid ball of radius r centered at the origin carrying a charge density rhor 1 kfracr2r2 for 0 le r le r where k is a constant a using gausss law find the electric field inside 34601

          1. Consider a solid ball of radius R centered at the origin carrying a charge density $\rho(r) = 1 + k\frac{r^2}{R^2}$ for $0 \le r \le R$, where k is a constant.
(a) Using Gauss's law, find the electric field inside and outside the ball.
(b) Find the electric potential inside and outside the ball, taking infinity as the reference point.
(c) Calculate the work required to assemble this charge distribution in two different ways:
i. Using $W = \frac{\epsilon_0}{2} \int_{\text{all space}} E^2 d\tau$.
ii. Using $W = \frac{1}{2} \int_D \rho V d\tau$.

$1 consider a solid ball of radius r centered at the origin carrying a charge density rhor 1 kfracr2r2 for 0 le r le r where k is a constant a using gausss law find the electric field inside 34601$

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