The electric intensity due to a dipole of length $10 \mathrm{~cm}$ and having a charge of $500 \mu…

The electric intensity due to a dipole of length $10 \mathrm{~cm}$ and having a charge of $500 \mu \mathrm{C}$, at a point on the axis at a distance $20 \mathrm{~cm}$ from one of the charges in air, is
  1. $6.25 \times 10^{7} \mathrm{~N} / \mathrm{C}$
  2. $9.28 \times 10^{7} \mathrm{~N} / \mathrm{C}$
  3. $13.1 \times 10^{11} \mathrm{~N} / \mathrm{C}$
  4. $20.5 \times 10^{7} \mathrm{~N} / \mathrm{C}$

Solution

We know, \(\mathrm{E}=9 \times 10^9 \cdot \frac{2 \mathrm{pr}}{\left(\mathrm{r}^2-1^2\right)^2}\) where \(\mathrm{p}=\left(500 \times 10^{-6}\right) \times\left(10 \times 10^{-2}\right)=5 \times 10^{-5} \mathrm{Cm}\) \(\begin{aligned} \mathrm{r} & =25 \mathrm{~cm}=0.25 \mathrm{~m}, 1=5 \mathrm{~cm}=0.05 \mathrm{~m} \\ \mathrm{E} & =\frac{9 \times 10^9 \times 2 \times 5 \times 10^{-5} \times 0.25}{\left\{(0.25)^2-(0.05)^2\right\}^2} \\ & =6.25 \times 10^7 \mathrm{~N} / \mathrm{C} \end{aligned}\)

Asked in: JEE Mains - Electrostatics - Test 5

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