Please help A rod of total charge q and length L sits on the

A rod of total charge +q and length L sits on the x-axis as shown above. What is the electric field at pointt P, a distance d on the y axis?

Solution

the distance from both ends of the rod to the point p is,

   r = sqrt[(L/2)² + d²] = sqrt[L² /4) + d²]

from figure we have

cos@ = (L/2)/r = L / 2sqrt[L² /4) + d²]

the net electric field along the x-direction is,

Ex = E sin@ - Esin@

       = 0

the net electric field along the y-axis is,

   Ey = E cos@ + E cos@

        = 2Ecos@

        = 2 [k*lambda /d] [L / 2sqrt[L² /4) + d²] ]

        = [2k*lambda /d] [L / sqrt[L² + 4d²] ]

      = [2k*(q/L) /d] [L / sqrt[L² + 4d²] ]

        = {2kq/d}[1 / sqrt[L² + 4d²]]