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(B) Let the vertices of the equilateral triangle be $A, B,$ and $C$. Let charges $Q$ be placed at each vertex. Let $P$ be the midpoint of side $BC$.Th

Vedclass · Accepted Answer

$\frac{Q}{{2\pi { \in _0}d}}\left[ {2 + \frac{1}{{\sqrt 3 }}} \right]$

Vedclass · Answer

(B) Let the vertices of the equilateral triangle be $A, B,$ and $C$. Let charges $Q$ be placed at each vertex. Let $P$ be the midpoint of side $BC$.The distance from $P$ to the vertices $B$ and $C$ is $r_1 = r_2 = d/2$.The distance from $P$ to vertex $A$ is the altitude of the triangle,$h = \frac{\sqrt{3}}{2}d$.The total potential at $P$ is the sum of potentials due to the three charges: $V_P = V_A + V_B + V_C$.$V_P = \frac{1}{4\pi \epsilon_0} \left( \frac{Q}{h} + \frac{Q}{d/2} + \frac{Q}{d/2} \right) = \frac{Q}{4\pi \epsilon_0} \left( \frac{1}{\frac{\sqrt{3}}{2}d} + \frac{2}{d} + \frac{2}{d} \right)$.$V_P = \frac{Q}{4\pi \epsilon_0 d} \left( \frac{2}{\sqrt{3}} + 4 \right) = \frac{Q}{2\pi \epsilon_0 d} \left( \frac{1}{\sqrt{3}} + 2 \right)$.

The side length of an equilateral triangle is $d$. Three charges,each of magnitude $Q$,are placed at the three vertices. If $P$ is the midpoint of one side,find the electric potential $V_P$ at point $P$.

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