Import Question JSON

Current Question (ID: 20117)

Question:

$\text{A point dipole with dipole moment } \vec{p} = -p_0 \hat{i} \text{ is placed at the origin.}$ $\text{What are the electric potential and electric field due to this dipole at a point located on the } y\text{-axis at a distance } d \text{ from the origin? (assume } V = 0 \text{ at infinity)}$

Options:

1. $\frac{|\vec{p}|}{4\pi\varepsilon_0 d^2}, \frac{-\vec{p}}{4\pi\varepsilon_0 d^3}$
2. $0, \frac{-\vec{p}}{4\pi\varepsilon_0 d^3}$
3. $\frac{|\vec{p}|}{4\pi\varepsilon_0 d^2}, \frac{\vec{p}}{4\pi\varepsilon_0 d^3}$
4. $0, \frac{\vec{p}}{4\pi\varepsilon_0 d^3}$

Solution:

$\text{Hint: Potential on equatorial point is zero.}$ $\text{Step 1: Draw the diagram.}$ $\text{Step 2: Find the potential at the distance } d \text{ on the } y\text{-axis.}$ $V_A = 0 \text{ V}$ $\text{Potential due to a dipole vanishes on the equatorial line.}$ $\text{Step 3: Find the electric field at the distance } d \text{ on the } y\text{-axis.}$ $E_A = -\frac{k\vec{P}}{d^3}$ $\Rightarrow E_A = -\frac{\vec{P}}{4\pi\varepsilon_0 d^3}$ $\text{Hence, option (2) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}