KVPY SA Exam 19-Nov-2017 Question Paper

Question : 22 of 80

Marks: +1, -0

A total charge q is divided as

q_1

and

q_2

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 = q_1 /q

. Choose the correct figure.

Validate

Solution:

E_\net = E_1↖{→}+E_2↖{→}

q = q_1 + q_2

{|E ↖{→}_\net|}=√{ ({kq_1}/a)^2+({kq_2}/a)^2+{2k^2q_1q_2}/a^2 .\cos 60°}

\E_\net=k/a√{q_1^2+q_2^2+q_1q_2}

\E_\net=k/a√{q_1^2+(q-q_1)^2+q_1(q-q_1)}

=k/{aq}×√{(q_1/q)^2+1^2+(q_1/q)^2-{2q_1}/q+q_1/q-q_1^2/q^2}

=k/{aq}√{x^2+1-x}

\E_\net=k/{aq}(√{(x-1/2)^2+3/4})

Minima must be at

|x = 1/2|

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