Two charges $q_{1}$ and $q_{2}$ are placed $30\ cm$ apart, as shown in the figure. A third charge $q_{3}$ is moved along the arc of a circle of radius $40\ cm$ from $C\ to\ D$. The change in the potential energy of the system is $\frac{q_{3}}{4\pi\varepsilon_{0}}k,$ where $k$ is [image:1_image202.emf]

Question

Dr. Abubacker · Accepted Answer

(a) Change in potential energy $(\mathrm{\Delta}U) = U_{f} - U_{i}$
[image:1_image382.emf]
$\Rightarrow \mathrm{\Delta}U = \frac{1}{4\pi\varepsilon_{0}}\left\lbrack \left( \frac{q_{1}q_{3}}{0.4} + \frac{q_{2}q_{3}}{0.1} ight) - \left( \frac{q_{1}q_{3}}{0.4} + \frac{q_{2}q_{3}}{0.5} ight) ightbrack$
$\Rightarrow \mathrm{\Delta}U = \frac{1}{4\pi\varepsilon_{0}}\left\lbrack 8q_{2}q_{3} ightbrack = \frac{q_{3}}{4\pi\varepsilon_{0}}(8q_{2})$
$	herefore k = 8q_{2}$

Q. Two charges $q_{1}$ and $q_{2}$ are placed $30\ cm$ apart, as shown in the figure. A third charge $q_{3}$ is moved along the arc of a circle of radius $40\ cm$ from $C\ to\ D$. The change in the potential energy of the system is $\frac{q_{3}}{4\pi\varepsilon_{0}}k,$ where $k$ is

Explanation

Reviewed by Dr. Abubacker

Want more practice?