Question

Two small, identical spheres having $+Q$ and $-Q$ charge are kept at a certain distance $F$ force acts between the two. If in the middle of two spheres, another similar sphere having $+Q$ charge is kept, then it experiences a force in magnitude and direction as

• A. Zero having no direction
• B. $8F$ towards $+Q$ charge
• C. $8F$ towards $-Q$ charge
• D. $4F$ towards $+Q$ charge

Answer 1

The correct option is C $8F$ towards $-Q$ charge

$F=F_{AB}=\frac{1}{4\pi {\epsilon }_0}.\left(\frac{-Q^2}{r^2}\right)$

$F^{\prime }=F_{AO}+F_{OB}=\frac{1}{4\pi {\epsilon }_0}.\left(\frac{4Q^2}{r^2}\right)+\frac{1}{4\pi \epsilon }.\left(\frac{-4Q^2}{r^2}\right)=4F+4F=8F$ [-ve sign indicates attractive force]

The sphere experiences $8F$ force towards $(-Q)$ charge.