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2. [30 pt=9+6+9+6] A non-conducting cylinder with radius $a$ has a linear charge density $\lambda$ ($\lambda$ > 0) uniformly distributed throughout the cylinder. It is surrounded by a conducting thin-shell cylinder (thickness $\sim \delta$) of radius $2a$. The thin shell is neutral initially, before the inner cylinder is slowly inserted. See Figure 2. Figure 2 (a) Find the electric field $E$, in terms of $r$, $\lambda$, and $a$, at radial distance $r$ from the center of the cylinder for (a1) $r \le a$, (a2) $a \le r \le 2a - \delta$, (a3) $2a - \delta < r < 2a$, and (a4) $r \ge 2a$. (b) Plot $E$ as a function of $r$ for the range $0 \le r \le 3a$. (c) Assuming that the electric potential at $r = 3a$ is $V_0$, find the electric potential $V$ in each region, as specified in (a) in a range of $0 \le r \le 3a$. (d) Plot $V$ as a function of $r$ for $0 \le r \le 3a$

          2. [30 pt=9+6+9+6] A non-conducting cylinder with radius $a$ has a linear charge density
$\lambda$ ($\lambda$ > 0) uniformly distributed throughout the cylinder. It is surrounded by a
conducting thin-shell cylinder (thickness $\sim \delta$) of radius $2a$. The thin shell is neutral
initially, before the inner cylinder is slowly inserted. See Figure 2.
Figure 2
(a) Find the electric field $E$, in terms of $r$, $\lambda$, and $a$, at radial distance $r$ from the center
of the cylinder for (a1) $r \le a$, (a2) $a \le r \le 2a - \delta$, (a3) $2a - \delta < r < 2a$, and
(a4) $r \ge 2a$.
(b) Plot $E$ as a function of $r$ for the range $0 \le r \le 3a$.
(c) Assuming that the electric potential at $r = 3a$ is $V_0$, find the electric potential $V$ in
each region, as specified in (a) in a range of $0 \le r \le 3a$.
(d) Plot $V$ as a function of $r$ for $0 \le r \le 3a$

2. [30 pt=9+6+9+6] A non-conducting cylinder with radius a has a linear charge density
λ (λ > 0) uniformly distributed throughout the cylinder. It is surrounded by a
conducting thin-shell cylinder (thickness ∼δ) of radius 2a. The thin shell is neutral
initially, before the inner cylinder is slowly inserted. See Figure 2.
Figure 2
(a) Find the electric field E, in terms of r, λ, and a, at radial distance r from the center
of the cylinder for (a1) r ≤ a, (a2) a ≤ r ≤ 2a - δ, (a3) 2a - δ < r < 2a, and
(a4) r ≥ 2a.
(b) Plot E as a function of r for the range 0 ≤ r ≤ 3a.
(c) Assuming that the electric potential at r = 3a is V0, find the electric potential V in
each region, as specified in (a) in a range of 0 ≤ r ≤ 3a.
(d) Plot V as a function of r for 0 ≤ r ≤ 3a

Added by Colleen G.

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