Electrostatics Question 678
Two charges q and -3q are placed fixed on x-axis separated by distance d. Where should a charge experience any force?
Options:
A) $ \frac{d-\sqrt{2}d}{2} $
B) $ \frac{d+\sqrt{3}d}{2} $
C) $ \frac{d+3d}{2} $
D) $ \frac{d-\sqrt{5}d}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
Let a charge 2q be placed at P, at a distance r from A where charge q is placed, .
The charge 2q will not experience any force, when the force of repulsion on it due to q is balanced by the force of attraction on it due to -3q at B where $ AB=d $
or $ \frac{( 2q )( q )}{4\pi {\varepsilon _{0}}{{\ell }^{2}}}=\frac{( 2q )( -3q )}{4\pi {\varepsilon _{0}}{{( \ell +d )}^{2}}} $
$ = 11,\mu\text{C}. $
$ \therefore \ell =\frac{2d\pm \sqrt{4d^{2}+2d^{2}}}{4}=\frac{d}{2}\pm \frac{\sqrt{3}d}{2} $
BETA
