A total charge q is divided as q₁ and q₂ which are kept at two of the vertices of an equilateral triangle of side a. The magnitude of the electric field E at the third vertex of the triangle is to be depicted schematically as a function of

Question

A total charge q is divided as q₁ and q₂ which are kept at two of the vertices of an equilateral triangle of side a. The magnitude of the electric field E at the third vertex of the triangle is to be depicted schematically as a function of x=q₁ / q . Choose the correct figure.

Quantrex Academy · Accepted Answer

Correct answer: 2

array l E_ n e t = E ₁+ E ₂ q=q₁+q₂ | E _ net |= ( k q₁ a )²+ ( k q₂ a )²+ 2 k² q₁ q₂ a² 60^ E_ n e t = k a q₁²+q₂²+q₁ q₂ E_ n e t = k a q₁²+ (q-q₁ )²+q₁ (q-q₁ ) array aligned &= k a q ( q₁ q )²+1²+ ( q₁ q )²- 2 q₁ q + q₁ q - q₁² q² &= k a q x²+1-x E_ n e t &= k a q ( (x-1 / 2)²+3 / 4 ) aligned Minima must be at | x =1 / 2|

A total charge q is divided as q₁ and q₂ which are kept at two of the vertices of an equilateral triangle of side a. The magnitude of the electric field E at the third vertex of the triangle is to be depicted schematically as a function of x=q₁ / q . Choose the correct figure.

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