3 identical charges Q are arranged at the vertices of an equilateral triangle .The side if the triangle is a. Find the intensity of the field at the vertex of a regular tetrahedron of which the triangle is the base?

hi,

 see the figure below

 h1= √3/2 a

h2 = ,√2/3 a

 E1 = 1/4¶ε  Q ( a/2i + h1/3 j + h2 k  )/ a^3                            { E =  1/4¶ε  Q  r  / r^3 }

E2 = 1/4¶ε  Q [( a/2i + h1/3 j + h2 k  ) - ( ai + 0j + 0k ) ] / a^3

     = 1/4¶ε  Q [(- a/2i + h1/3 j + h2 k  )] /a^3

E3 = 1/4¶ε  Q [( a/2i + h1/3 j + h2 k  ) - ( a/2 i + h1 j + 0k) ]/ a^3

     = 1/4¶ε  Q [( -2 h1/3 j + h2 k  )]/a^3

total field = E1 +E2 +E3

               =   1/4¶ε  Q [  0 i +  0j  + 3 h2 k ] /a^3

               =   1/4¶ε  Q  √6  / a^2