Import Question JSON

Current Question (ID: 20368)

Question:

$\text{Electric field is applied along } +\hat{y} \text{ direction. A charged particle is travelling along } -\hat{k}, \text{ undeflected. Then magnetic field in the region will be along?}$

Options:

1. $\hat{i}$
2. $-\hat{i}$
3. $\hat{j}$
4. $-\hat{k}$

Solution:

$\text{If the charged particle is moving in both uniform electric and magnetic field with no deflection then force will be zero on charged particle.}$ $q \left( \vec{E} + \vec{v} \times \vec{B} \right) = 0$ $\left( \vec{v} \times \vec{B} \right) = -\vec{E}$ $\left( v_0 \left( -\hat{k} \right) \times \vec{B} \right) = -E_0 \hat{j}$ $\vec{B} \text{ should be in } \hat{i} \text{ direction to balance the electrostatic force on the charge particle. (Assuming the given charge to be positive.)}$

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
}