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If three charges q are placed at corners of equilateral triangle than what should be the magnitude of Q placed at center O so that the system remains stationary.

Asked by sudheerkapoor67 5th November 2017, 7:20 PM
Answered by Expert
Answer:
 
Let us assume the charges placed at corner are positive and equal magnitude q.

At Center O, any charge will get balanced because equal magnitude forces(either repulsion or attraction)
and angle between them also equal (120°). 
 
If we see the forces at corner of the given equilateral triangle, The charge placed at center o should be negative.
 
Then only the resultant force FR due to F1 and F2 will be balanced by F3 which is in the opposite direction of FR.
 
if we equate the magnitude of FR and FQ, we will get the magnitude of Q in terms of q.
 
begin mathsize 12px style open vertical bar F R close vertical bar space equals space open vertical bar F 3 close vertical bar

2 fraction numerator q squared over denominator 4 pi epsilon subscript 0 a squared end fraction space cos 30 space equals space fraction numerator 3 q Q over denominator 4 pi epsilon subscript 0 a squared end fraction

b y space s i m p l i f y i n g space w e space w i l l space g e t space Q space equals space fraction numerator q over denominator square root of 3 end fraction end style
It is assumed here the side of triangle is a and the distance OC = a/√3
Answered by Expert 13th December 2017, 7:46 PM
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