Question

If two like charges of magnitude $1\times {10}^{-9}$ coulomb and $9\times {10}^{-9}$ coulomb are separated by a distance of 1 meter, then the point on the line joining the charges, where the force experienced by a charge placed at the point is Zero, is:

• A. $0.25m$ from the charge $1\times {10}^{-9}$ coulomb
• B. $0.75m$ from the charge $9\times {10}^{-9}$ coulomb
• C. Both (a) and (b)
• D. At all points on the lines joining the charges

Answer 1

Answer: (A), (B)

The correct options are
A $0.25m$ from the charge $1\times {10}^{-9}$ coulomb
B $0.75m$ from the charge $9\times {10}^{-9}$ coulomb

Charges $=1\times {10}^{-9}C$ and $9\times {10}^{-9}C$

distance $=1m$

$F=0$

or, $\frac{1}{4\pi {ϵ}_0}\times \frac{q_1{q}_2}{r^2}=0$

or, $9\times {10}^9\times \frac{1\times {10}^{-9}\times 9\times {10}^{-9}}{1^2}$

or, $8.1\times {10}^{-8}N$

$8.1\times {10}^{-8}=9\times {10}^9\times \frac{1\times {10}^{-9}\times q_2}{1^2}$

or, $q=9\times {10}^{-3}$

and then, the distance

$8.1\times {10}^{-8}=9\times {10}^9\times \frac{1\times {10}^{-9}\times 9\times {10}^{-9}}{(1-x)}$

or, $x=0.75m$

Distance from charge $1\times {10}^{-9}=1-x=1-0.75=0.25$