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CBSE Class 12-science Answered

Determine the potential energy of the configuration ? Answer is written in the pic but how it is even possible 
question image
Asked by govtsecschoolnayaganv051 | 29 Sep, 2019, 06:44: PM
answered-by-expert Expert Answer
Final answer you have shown is -ve . It means that some of the charges are -ve.
But you have not mentioned sign of charges in diagram.
 
If we assume any two charges in adjacent vertices in the square are -ve,
then we get the final potential value as shown in your figure.
 
Let charges q1 , q2 , q3 and q4 are placed in a square of side a, as shown in figure.
 
Potential of given charge configuration is given by
 
V = K × [  ( q1q2/a ) + ( q2q3/a )+ ( q1q3/(a√2) ) + ( q1q4/a ) + ( q3q4/a ) + ( q1q3/(a√2) ) ] Volt  ...............................(1)
 
where K = 1/(4πεo)   and εo is the permittivity of free space
 
If we substitute,  q1 = q2 = -q   and  q3 = q4 = q
 
Then potential is given by, 
 
V = K × [  ( q2 /a ) - ( q2 /a ) - ( q2/(a√2) ) - ( q2/a ) + ( q2/a ) - ( q2 /(a√2) ) ] = - 2K( q2/(a√2) )  Volt  ...............................(2)
 
V =  [ q2 / ( 4πεo a ) ] ( -√2 )  Volt
 
 
Answered by Thiyagarajan K | 30 Sep, 2019, 11:52: AM

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