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Electric charges 1 \mu \mathrm{C},-1 \mu \mathrm{C} and  2 \mu \mathrm{C} are placed at air in corner \mathrm{A}, \mathrm{B}, \mathrm{C} respectively of an equilateral triangle \mathrm{ABC} of sides, 10 \mathrm{~cm}. Find the resultant force on charge at \mathrm{C}.

Option: 1

1.8 \mathrm{~N}


Option: 2

0.9 \mathrm{~N}


Option: 3

2.7 \mathrm{~N}


Option: 4

0 \mathrm{~N}


Answers (1)

best_answer

Given: 

Charge at A, q_1=1 \mu C

Charge at B, q_2=1 \mu C

Charge at C, q_3=2 \mu C

Side length of the equilateral triangle,  A B=B C=C A=10 \mathrm{~cm}

F_A=  force on C due to charge placed at

A =9 \times 10^9 \times \frac{10^{-6} \times 2 \times 10^{-6}}{\left(10 \times 10^{-2}\right)^2}=1.8 \mathrm{~N}
F_B=  force on C due to charge placed at 

B =9 \times 10^9 \times \frac{10^{-6} \times 2 \times 10^{-6}}{(0.1)^2}=1.8 \mathrm{~N}

Net force on C

F_{\text {net }}=\sqrt{\left(F_A\right)^2+\left(F_B\right)^2+2 F_A F_B \cos 120^{\circ}}=1.8 \mathrm{~N}

Posted by

rishi.raj

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