Two semicircular rings lying in same plane, of uniform linear charge density `lambda` have radius r and 2r. They are joined using two straight uniformly charged wires of linear charge density `lambda` and length r as shown in figure. The magnitude of electric field at common centre of semi circular rings is -

Options

A. `1/(4piepsilon_(0))(3lambda)/(2r)`
B. `1/(4piepsilon_(0))(lambda)/(2r)`
C. `1/(4piepsilon_(0))(2lambda)/r`
D. `1/(4piepsilon_(0))(lambda)/r`

Answer

D

Explanation

The electric field due to both straight wires shall cancel at common centre O, the electric field due to larger and smaller semi circular rings at O be E and E' respectively.
`E=1/(4piepsilon_(0))(2lambda)/(2r), E'=1/(4piepsilon_(0))(2lambda)/r`
`:.` Magnitude of electric field at O is
`=E'-E=1/(4piepsilon_(0))((2lambda)/r-(lambda)/r)=1/(4piepsilon_(0))(lambda)/r`