Question

. There are two line charges each of length "L" having the same
line charge density, with one kept along the y-axis from (0,0)
to (0,a) and the other parallel to the former from (2a,0) to
(0,a). Evaluate the electric field due to both these line charges
at the point (a,0)​

Answer 1

Answer:

The electric field E is measured at a point P(0, 0, d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List - I contains different relations between E and d. List - II describes different electric charge distributions, along with their locations. Match the functions in List - I with the related charge distributions in List - II

List - IList - II(P) E is independent of d(1) A point charge Q at the origin(Q) E∝d1(2) A small dipole with point charges Q at (0,0,l) and - Q at (0, 0, -l). Take 2l<<d(R) E∝d21(3) A infinite line charge coincident with the x-axis, with uniform linear charge density λ.(S) E∝d31(4) Two infinite wires carrying uniform linear charge density parallel to the x-axis. The one along (y=0,z=l) has a charge density + λ and the one along (y=0,z=−l) has a charge density −λ. Take 2l<<d(5) Infinite plane charge coincident with the xy-plane with uniform surface charge density.

(i) E = d2KQ⇒E∝d21

(ii) Dipole

  E=d32kp1+3cos2θ

  E∝d31 for dipole

(iii) For line charge

    E=d2kλ

     E∝d1

 (iv) E = d−12Kλ−d+l2Kλ

           =2Kλ[d2–l2d+l−d+l]

       E=d2[1−d2l2]2Kλ(2l)

         E∝d21

  (v) Electric field due to sheet

       ϵ=2ϵ