for a conservative field ….....,,,,,.,.,. .,......∫E.dl=? .. and why

The vanishing of closed line integrals means that the field is conservative.

Since∮→E⋅d→l" id="MathJax-Element-8-Frame" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;" tabindex="0"> 


→ld⋅→E∮ is equivalent to→∇×→E=0" id="MathJax-Element-9-Frame" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-stretch: inherit; line-height: normal; font-family: inherit; vertical-align: baseline; display: inline; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; position: relative;" tabindex="0">



0=→E×→∇, the "physical interpretation" is the the electric field is irrotational, i.e. it has no "vortices". The, more valuable, mathematical implication is that there is a scalar potential whose gradient is the electric field.