A non-conducting ring of radius `0.5 m` carries a total charge of `1.11xx10^(-10)`C distributed non-uniformly on its circumference producing an electric field E everywhere is space. The value of the integral `int_(l=oo)^(l=0)-E.dI (l=0` being centre of the ring) in volt is

Options

A. `+2`
B. `-1`
C. `-2`
D. zero

Answer

A

Explanation

`int_(1=infty)^(1=0)vec(E).hatdhatI=int_(1=infty)^(1=0)dV=V`(centre) - V(infinity) but V (infinity)=0
`therefore" "int_(1=infty)^(1=0)vecE.hatdhatI` corresponds to potential at centre of ring
and V(centre)`=(1)/(4piepsi_(0)).(q)/(R)=((9xx10^9)(1.11xx10^(-10)))/(0.5)=2V`