A continuous line of charge of length 3d lies along the x-axis, extending from x + d to x + 4d, The line carries a uniform linear charge density `lambd` . In terms of `d, lambda` and any necessary physical constant find the magnitude of the electric field at the origin.

Options

A. `lambda//5 pi epsi_(0) d`
B. `lambda // 4 pi epsi_(0) d`
C. `3 lambda //16 pi espi_(0)d`
D. `3 lambda // 8 pi epsi_(0)d`

Answer

C

Explanation

Electric field at origin can be given by intergrating the electric fkeld due to an element considered on the rod of length dx at a distance x from origin which is given as
`E= int_a ^(4d) (k lamda dx)/x^2 implies E= lamda/(4pi e_0) -1/x |_d^(4d) =lamda/(4 pi e_0) (1/d-1/(4d))=(3 lamda)/(16 pi e_0d)`