Two charges $+\mathrm{q}$ and $-\mathrm{q}$, each $1 \mu \mathrm{C}$ are arranged as shown in the figure. If…

Two charges $+\mathrm{q}$ and $-\mathrm{q}$, each $1 \mu \mathrm{C}$ are arranged as shown in the figure. If $x=2 \mathrm{~cm}$ and $y=3 \mathrm{~cm}$ then potential difference $\left(V_A-V_B\right)$ is
  1. $5.4 \times 10^2 \mathrm{~V}$
  2. $5.4 \times 10^5 \mathrm{~V}$
  3. $5.2 \times 10^2 \mathrm{~V}$
  4. $2.7 \times 10^5 \mathrm{~V}$

Solution

Distance between two charge, $d=2 x+y$ $ =2 \times 2+3=7 \times 10^{-2} \mathrm{~m} $ Potential at $A, V_A=\frac{1}{4 \pi \epsilon_0} \frac{q}{d}$ $ =9 \times 10^9 \times \frac{1 \times 10^{-6}}{7 \times 10^{-2}} $ Potential at $B, V_B=\frac{1}{4 \pi \epsilon_0} \frac{-q}{d}$ $ =-9 \times 10^9 \times \frac{10^{-6}}{7 \times 10^{-6}} $ $ V_A-V_B=2 \times 9 \times 10^{-9} \times \frac{10^{-6}}{7 \times 10^{-6}}=2.7 \times 10^5 \mathrm{~V} $

Asked in: AP EAMCET 2023 (19 May Shift 1)

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