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Three point charges q, 2q and 8q are to ...

Three point charges q, 2q and 8q are to be placed on a
. 9cm long straight line. Find the
. positions where the charges shouldbe placed such that the potential energy
. of this sysrem is minimum. In this situation, what is the
. electric field at the charge q due to the other two charges?

Text Solution

Verified by Experts

The correct Answer is:
3 CM 0
For potential energy to be minimum the bigger charges should be farthest. Let x be the distance of q from 2q. Then potential energy of the system shown in figure would be
`U=K[((2q)(q))/x+((8q)(q))/((9-x))=((2q)(q))/9],Here K=1/(4pi epsilon_0)`
For U to be minimum `2/x+8/(9-x)` should be minimum.
v\`d/(dx)[2/x+8/(9-x)]=0 :.(-2)/x^2+8/((9-x)^2)=0 :.x/(9-x)=1/2 or x=3 cm`
i.e., distance of charge q from 2q should be 3 cm. Electric field at q
`E=(K(2q))/((3xx10^(-2))^2)-(K(8q))/((6xx10^(-2))^2)=0`
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