91Ó°ÊÓ

A hollow soda straw that has been uniformly charged with a positive charge.

To find the electric field vector of the whole body which contains charge, the procedure of Gauss is to be adopted.

$→$Any charged object can be considered as made up of tiny symmetric parts.

$→$For a tiny part, evaluate the electric flux at a point where the electric field is to be computed.

$→$Integrate over all the similar parts to get the total or resultant electric flux.

$→$Consequently, the field vector $\underset{E}{→}$of the whole body can be obtained from role="math" localid="1648580930633" $\left.∫âˆ\dots =∫\frac{Q}{{\mathrm{Ï\mu }}_0}=∫\stackrel{→}{(E}·dS\right)$

Now adopting the Gauss method for the present scenario step by step

$→$The straw is being made up of many symmetric rings of positive chargeQ.

$→$Computing the field vector $\underset{E}{→}$due to each ring at the center is found to be $\stackrel{→}{E}=\frac{Q}{4\mathrm{Ï€}{\mathrm{Î\mu }}_0{r}^2}$where,r is the distance of the center from the ring in the study.

$→$Integrating all field vectors $\underset{E}{→}$emanated from all segments gives a resultant electric field equal to zero. This is due to the fact that the left and right parts of the center are symmetric and hence field vector cancels out giving rise to the resultant field as zero.