A circular wire-loop of radius a carries a total charge Q distributed uniformly over its length . A small length dL of the wire is cut off. Find the electric field at the centre due to remaining wire.

Options

A. `(QdL)/(8 pi epsilon_(0)a^(3))`
B. `(QdL)/(4 pi epsilon_(0)a^(3))`
C. `(QdL)/(2 pi epsilon_(0)a^(3))`
D. `(QdL)/( pi epsilon_(0)a^(3))`

Answer

1

Explanation

Charge on `dL , Q' = (Q dL)/(2 pi a)`
`E_(0) = (1)/(4 pi in_(0)) (Q')/(a^(2))`
`= (1)/(4 pi in_(0)) .(QdL)/(2 pi a^(3))`
`= (QdL)/(8 pi^(2) in_(0) a^(3))`