Question

A long cylindrical volume contains a uniformly distributed charge of density rho. Find the electric field at a point P inside the cylindrical volume at a distance x from its axis (figure 30-E5).
Figure

Answer 1

Answer:

it will be x -2 x n/6. By the way I would suggest to remember the formulas

Answer 2

A long cylindrical volume contains a uniformly distributed charge of density rho E=ρ$\times$2 ∈0

Explanation:

• Inside the cylinder, the Volume charge density = ρρ
• Say, the radius of the cylinder be r
• Say, charge enclosed by the given cylinder be Q
• Let's take into consideration a Gaussian cylindrical surface of radius x and height h.
• Say, charge enclosed by the cylinder of radius $\times$ be q′q'.
• Note that the charge on this imaginary cylinder can be found by considering the product of the volume charge density of the cylinder and the volume of the imaginary cylinder.  

Hence,

$q^{\prime} q^{\prime}=\rho(\pi \times 2 h) \rho \pi \times 2 h$

As per Gauss's Law,

$\oint \mathrm{E} \cdot \mathrm{d} \mathrm{s}=\mathrm{qen} \in 0 \mathrm{E} \cdot 2 \pi \mathrm{xh}=\rho(\pi \times 2 \mathrm{h}) \in 0 \mathrm{E}=\rho \times 2 \in 0$