Question

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

Answer 1

Correct Answer - a
From definition of potential differecne `overset(1=0)underset(1=oo)intE.d1=potential` difference at infinity and at centre of ring `=(V_(centre)=V_(infinity))`
But by convention `V_(infinity)=0 and V_(centre)=(1)/(4piepsilon_(0))(q)/(R )`
`=9xx10^(9)xx(1.11xx10^(-10))/(0.5)=2 volt`
`therefore overset(1=0)underset(1=oo)(E.di)=2 volt-0 volt =2 volt`