Ten charges are placed on the circumference of a circle

Question:

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

(Take $V=0$ at infinity)

  1. $\mathrm{V}=\frac{10 \mathrm{q}}{4 \pi \epsilon_{0} \mathrm{R}} ; \mathrm{E}=\frac{10 \mathrm{q}}{4 \pi \epsilon_{0} \mathrm{R}^{2}}$

  2. $\mathrm{V}=0, \mathrm{E}=\frac{10 \mathrm{q}}{4 \pi \in_{0} \mathrm{R}^{2}}$

  3. $\mathrm{V}=0, \mathrm{E}=0$

  4. $\mathrm{V}=\frac{10 \mathrm{q}}{4 \pi \epsilon_{0} \mathrm{R}} ; \mathrm{E}=0$

Correct Option: , 3

Solution:

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