Question

Three point charges of charge $q,2q$ and $8q$ can be placed on a $9cm$ long straight line. Any two charges can be placed on the two ends of the line and a third charge anywhere in between. Then, the potential energy of the system will be minimum when the charges are placed as follows

• A. $q$ and $8q$ on ends and $2q$ anywhere in between
• B. $q$ and $2q$ on ends and $8q$ anywhere in between
• C. $2q$ and $8q$ on ends and $q$ at a point in between where the electric field due to $2q$ and $8q$ is zero
• D. $q$ and $2q$ on ends and $8q$ at a point in between where the electric filed due to $q$ and $2q$ is zero

Answer 1

Answer: (C)

$2q$ and $8q$ on ends and $q$ at a point in between where the electric field due to $2q$ and $8q$ is zero

The potential energy will be minimum when the potential due to any two higher magnitude positive charges is minimum i.e. $2q$ and $8q$ are placed at the ends.
The $q$ charge should be placed such that it's potential energy will be minimum that indicates charge $q$ should be in equilibrium which implies point where electric field of $2q$ and $8q$ is zero.