Question

Consider a uniformly charged thin-walled right circularcylindrical shell having total charge Q, radiusR, and height h. Determine the electric field ata point a distance d from the right side of the cylinderas shown in the figure below. (Use k_e for ke,Q, d, R, and h as necessary.) Suggestion: Use the followingexpression and treat the cylinder as a collection of ring charges.

Answer 1

Answer:

$\frac{k_eQ}{2h}$

Explanation:

The question is missing an image. I have added this as an attachment to my answer.

Given;

Q = total charge

R = radius of cylindrical shell

h = height of cylindrical shell

d = distance of point from the right side of the cylinder

Let the thickness of the cylindrical shell be $dx$ , and the charge  $\frac{Qdx}{h}$,

Now, using the formula for finding the electric field due to a ring at a chosen point:

$dE = \frac{k_ex}{(x^2 + R^2)^{\frac{3}{2}}} {\frac{Qdx}{h}i}$

where $x$ = center of the ring to the point

$k_e$ = electrostatic constant

We integrate on both sides from the limits $d$ to $d + h$  in order to determine the electric field at the point $E$

$\int\limits dE$ = $\int\limits^{d + h}_d {\frac{k_eQxdx}{h(x^2 + R^2)^{\frac{3}{2}}}i}$

$E = \int\limits^{d + h}_d {\frac{k_eQdx}{h(x^2 + R^2)^{\frac{3}{2}}}i} = \frac{k_eQ}{2h}$