The side length of an equilateral triangle is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $P$.

Similar Questions

The potential of a large liquid drop formed when eight identical small liquid drops are combined is $20 \,V$. What was the potential of each single small drop (in $\,V$)?

Three concentric metal shells $A, B$ and $C$ of respective radii $a, b$ and $c$ $(a < b < c)$ have surface charge densities $+\sigma, -\sigma$ and $+\sigma$ respectively. The potential of shell $B$ is

$A$ hollow metallic sphere of radius $R$ is given a charge $Q$. Then the potential at the centre is

An electric charge $10^{-8} \ C$ is placed at the point $(4 \ m, 7 \ m, 2 \ m)$. At the point $(1 \ m, 3 \ m, 2 \ m)$,the electric

The work done to take an electron from rest where potential is $-60\, V$ to another point where potential is $-20\, V$ is given by.....$eV$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module