In a figure shown find the ratio of the linear charge densites `lambda_(1)` (on semi-infinite straight wire) and `lambda_(2)` (on semi-circular part) that is, `lambda_(1)//lambda_(2)` so that the field at `O` is along `y` direction.

Options

A. `2`
B. `1.5`
C. `3`
D. `2.5`

Answer

a

Explanation

Electric field due to semicircular part:
`E_(2)=(lambda_(2))/(2pi epsilon_(0)R)`

Electric field due to straight part:
`E_(1x)=E_(1y)= (lambda_(1))/(4pi epsilon_(0)R)`
For net field to be along `y`-axis:
`E_(2)=E_(1x)implies (lambda_(2))/(2pi epsilon_(0)R)=(lambda_(1))/(4pi epsilon_(0)R) rArr (lambda_(1))/(lambda_(2))=2`