Question

Two identical rings of radii $0.1m$ are placed co-axially at a distance $0.5m$ apart. The charges on the rings are $2\mu C$ and $4\mu C$ respectively. The work done in transferring $5\mu C$ charge from centre of one ring to other is

• A. $0.75J$
• B. $0.90mJ$
• C. $1.05J$
• D. $1.26J$

Answer 1

The correct option is A $0.75J$

The $Q_0=5uc$ is transfered from $A\to B,d=0.5m$ Potential due to a change ring at a distance $x$ from is centre is given by :- $V=\frac{KQ}{\sqrt{r^2+z^2}}$ where $K=\frac{1}{4\pi {\in }_0},r=0.1m$

Potential at centre $A$,

$V_A=\frac{K{q}_1}{r}+\frac{K{q}_2}{\sqrt{r^2+{\alpha }^2}}$ [Potential due to both rings]

$=9\times {10}^9(\frac{2\times {10}^{-6}}{0.1}+\frac{4\times {10}^{-6}}{\sqrt{{0.1}^2+0.562}})=2.5\times {10}^{5}V$

Similarly ar $B$,

$V_B=\frac{K{q}_2}{r}+\frac{K{q}_2}{\sqrt{r^2+{\alpha }^2}}$

$=9\times {10}^9(\frac{4\times {10}^{-6}}{0.1}+\frac{2\times {10}^{-6}}{\sqrt{{0.1}^2+{0.5}^2}})=3.95\times {10}^{5}V$

Thus work done

$W=Q_0(V_B-V_A)$

$=6\times {10}^{-6}\times (3.95\times {10}^5-2.5\times {10}^5)$

$\Rightarrow W=0.725\simeq 0.75J$