Question

Two point charges 1 μC and 9 μC are placed at x = –1 m and x = 3 m on x-axis. The position between two charges where net electric force on a unit test charge will be zero, is

Answer 1

It has given that two point charge 1μC and 9μC are placed at x = -1 m and x = 3m on axis.

we have to find the position between two charges where net electric force on a unit test charge will be zero.

(-1,0)1μC .............q A ................................9μC (3,0)

|-------------------------4-----------------------------|

let charge q is placed between two charge at point A.

now, force experienced by A , F_A = k(1μC)q/(x)²

force experienced by B, F_B = k(9μC)q/(4 -x)²

net force acting on charge q = F_A + F_B

= k(1μC)q/x²- k(9μC)q/(4 - x)² = 0

⇒1/x² = 9/(4 - x)²

⇒1/x = 3/(4 - x)

⇒4 - x = 3x

⇒x = 1

so, position of charge , q = (0, 0) [ because distance between 1μC and q is 1 if 1μC is placed at (-1,0) then q is placed at (0,0). ]

therefore the position between two charges where net electric force on a unit test charge will be zero, is origin.