Flag Electrostatics> Four charges equal to -Qare placed four c...
question mark

Four charges equal to -Qare placed four corners of a square and a charge q is at centre and whole system is in equillibrium .What is value of q?

Barsat Kher , 8 Years ago
Grade 10
anser 1 Answers
Vikas TU

Last Activity: 7 Years ago

We have the framework which comprise of 4 point charges +q set at 4 corners of a square . The four of charges will be in balance if add up to electric potential vitality is zero.Hence, = Potential Energy because of all the four sets in which Potential vitality framework charges put at the side of the sides of square+PE because of each one of those sets in which charges are set at finishes of the slanting of square +Potential Energy because of sets shaped by any charge at the corner and charge 
 
Potential Energy of System = 4×1/4πε0 ×q2/a +2×1/4πε0 × q2/a√2 +4×1/4πε0 × qQ/a/√2 
 
Potential Energy of System = 1/4πε0×4q/a [q+q/2√2+Q√2 ] 
 
The framework will be in balance if 
 
Potential Energy of System = 0 
 
1/4πε0 ×(4q/a) [q+ q/2√2+Q√2 ] = 0 
 
q+ q/2√2+Q√2 = 0 
 
Q√2 = −(q+q/2√2 ) 
 
Q = −(q/√2 + q/4) 
 
Q = −q((2√2+1 )/4) 
 
Q = −q/4 (2√2 +1) 
 
We have the framework which comprise of 4 point charges +q put at 4 corners of a square . The four of charges will be in balance if add up to electric potential vitality is zero.Hence, = Potential Energy because of all the four sets in which Potential vitality framework charges set at the edge of the sides of square+PE because of every one of those sets in which charges are set at finishes of the askew of square +Potential Energy because of sets shaped by any charge at the corner and charge 
 
Potential Energy of System = 4×1/4πε0 ×q2/a +2×1/4πε0 × q2/a√2 +4×1/4πε0 × qQ/a/√2 
 
Potential Energy of System = 1/4πε0×4q/a [q+q/2√2+Q√2 ] 
 
The framework will be in harmony if 
 
Potential Energy of System = 0 
 
1/4πε0 ×(4q/a) [q+ q/2√2+Q√2 ] = 0 
 
q+ q/2√2+Q√2 = 0 
 
Q√2 = −(q+q/2√2 ) 
 
Q = −(q/√2 + q/4) 
 
Q = −q((2√2+1 )/4) 
 
Q = −q/4 (2√2 +1)

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free