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CBSE Class 12-science Answered

Three charges of q,3q, and -2q are placed at the vertices of an equilateral triangle of side 20cm. If q is 2 microcoulomb, what work must be done to dissociate this system of charge?
Asked by lekhakarthikeyan | 21 Aug, 2018, 10:05: PM
answered-by-expert Expert Answer
 
Workdone to dissociate the system of given charge configuration is same as the workdone to assemeble the configuration.
Let q is the reference charge initially present at a vertex of equilateral triangle of side 20 cm.
Let us find the potential energy of -2q to place at another vertex of the given equilateral triangle.
 
W1 begin mathsize 12px style equals space fraction numerator negative 2 q squared over denominator 4 pi epsilon subscript 0 cross times 20 cross times 10 to the power of negative 2 end exponent end fraction end styleJoules
Now let us find the potential energy of 3q to place at the third vertex of the given triangle.
 
W2 begin mathsize 12px style equals space fraction numerator 3 q squared over denominator 4 pi epsilon subscript o cross times 20 cross times 10 to the power of negative 2 end exponent end fraction minus fraction numerator 6 q squared over denominator 4 pi epsilon subscript o cross times 20 cross times 10 to the power of negative 2 end exponent end fraction end styleJoules
workdone to assemble or dissociate the configuration is sum of the above potential energies.
 
workdone = w1 + W2 begin mathsize 12px style equals space fraction numerator q squared over denominator 4 pi epsilon subscript o cross times 20 cross times 10 to the power of negative 2 end exponent end fraction cross times open parentheses negative 2 plus 3 minus 6 close parentheses space equals space fraction numerator negative 5 q squared over denominator 4 pi epsilon subscript o cross times 20 cross times 10 to the power of negative 2 end exponent end fraction end style
if we substitute q = 2 μC and 1/(4πεo)  = 9×109 , we get total workdone = -0.9 Joules
Answered by Thiyagarajan K | 22 Aug, 2018, 06:40: AM

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