Electric charges of `1 mu C, 1 mu C `and `2mu`C are placed in air at the corners of A, B and C respectively of an equilateral triangle ABC having the length of the side 10 cm. The resultant force of C is `(1/4 pi epsilon_(0) = 9 xx 10^(9) N-m^(2)/C^(2))`

Options

A. 0.9 N
B. `1.8sqrt(3)`N
C. 2.7 N
D. 3.6 N

Answer

(b)

Explanation

Resultant Force at C is,F =`sqrt(F_(1)^(2) + F_(2)^(2) + 2F_(1)F_(2)costheta)`
`F_(1) =1/4pi epsilon_(0) q_(1)q_(2)/AC^(2)` = `9 xx 10^(9) (1 xx 10^(-6))/(10 xx 10^(-2)^(2))`
= 1.8 N
`F_(2) =1/4pi epsilon_(0) q_(1)q_(2)/BC^(2) = 9 xx 10^(9) (2 xx 10^(-6))/(10 xx 10^(-2)^(2))`
=1.8 N
`:. F = sqrt ((1.8)^(2) + (1.8)^(2) + 2(1.8)(1.8)cos60^(0)`
`= 1.8 sqrt(3)` N