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Current Question (ID: 20130)

Question:

$\text{Ten charges are placed on the circumference of a circle of radius } R \text{ with constant angular separation between successive charges.}$ $\text{Alternate charges } 1, 3, 5, 7, 9 \text{ have charge } (+q) \text{ each, while } 2, 4, 6, 8, 10 \text{ have charge } (-q) \text{ each.}$ $\text{The potential } V \text{ and the electric field } E \text{ at the centre of the circle are respectively: (Take } V = 0 \text{ at infinity)}$

Options:

1. $V = \frac{10q}{4\pi\varepsilon_0 R} ; E = \frac{10q}{4\pi\varepsilon_0 R^2}$
2. $V = 0, E = \frac{10q}{4\pi\varepsilon_0 R^2}$
3. $V = 0, E = 0$
4. $V = \frac{10q}{4\pi\varepsilon_0 R} ; E = 0$

Solution:

$\text{Hint: } V = \sum \frac{kQ}{r}$ $\text{Potential of centre } = V = \sum \left( \frac{kq}{R} \right)$ $V_C = \frac{K (\Sigma q)}{R}$ $V_C = \frac{K(0)}{R} = 0$ $\text{Electric field at centre } \vec{E}_B = \Sigma \vec{E}$ $\text{Let E be electric field produced by each charge at the centre, then resultant electric field will be}$ $E_C = 0, \text{ Since equal electric field vectors are acting at equal angle so their resultant is equal to zero.}$

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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
}