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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
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