Question 848: Electrostats & Capacitance

Question

Three charges each of value $$+q$$ are placed at the corners of an isosceles triangle $$\mathrm{ABC}$$ of sides $$\mathrm{AB}$$ and $$\mathrm{AC}$$ each equal to $$2 \mathrm{a}$$. The mid points of $$A B$$ and $$A C$$ are $$D$$ and $$E$$ respectively. The work done in taking a charge $$Q$$ from $$D$$ to $$E$$ is ( $$\varepsilon_0=$$ permittivity of free space)

Accepted Answer

$$	ext { Given } \mathrm{AB}=\mathrm{AC}=2 \mathrm{a}$$
$$\mathrm{V}_{\mathrm{D}}=\mathrm{V}_{\mathrm{E}}$$ $$(\because \mathrm{D}$$ and $$\mathrm{E}$$ are mid-points)
$$	herefore \quad$$ The work done in taking a charge $$\mathrm{q}$$ from $$\mathrm{D}$$ to $$\mathrm{E}$$ is
$$\mathrm{W}=\mathrm{q} \Delta \mathrm{V}=\mathrm{q}\left(\mathrm{V}_{\mathrm{D}}-\mathrm{V}_{\mathrm{E}}ight)$$
$$	herefore \quad \mathrm{W}=0$$ (Equipotential surfaces)

Answer

Zero

Answer

$$\frac{3 q \mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{a}}$$

Answer

$$\frac{\mathrm{qQ}}{8 \pi \varepsilon_0 \mathrm{a}}$$

Answer

$$\frac{3 \mathrm{qQ}}{8 \pi \varepsilon_0 \mathrm{a}}$$

Electrostats & Capacitance

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