A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it.

Question:

A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net field $\overrightarrow{\mathrm{E}}$ at the centre $\mathrm{O}$ is :- 

  1. $\frac{\mathrm{q}}{2 \pi^{2} \varepsilon_{0} \mathrm{r}^{2}} \hat{j}$

  2. $\frac{q}{4 \pi^{2} \varepsilon_{0} r^{2}} \hat{j}$

  3. $-\frac{\mathrm{q}}{4 \pi^{2} \varepsilon_{0} \mathrm{r}^{2}} \hat{\mathrm{j}}$

  4. $-\frac{q}{2 \pi^{2} \varepsilon_{0} r^{2}} \hat{j}$


Correct Option: , 4

Solution:

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