Question

Two particles with identical positive charges and a separation of $2.5\times {10}^{-2}m$ are released from rest. Immediately after their release, particle 1 has acceleration whose magnitude is $4\times {10}^{3}m{s}^{-2}$. Particle 1 has a mass of $9\times {10}^{-6}kg$. Then each of the particle has charge of :

• A. $3\times {10}^{-8}C$
• B. $4\times {10}^{-8}C$
• C. $5\times {10}^{-8}C$
• D. $6\times {10}^{-8}C$

Answer 1

The correct option is C $5\times {10}^{-8}C$

Force on particle 1 = mass X acceleration =$9\times {10}^{-6}kg\times 4\times {10}^{3}m{s}^{-2}=0.036N$
By Coulomb's law, this force $=\frac{1}{4\pi \epsilon o}\frac{q^2}{r^2}$, where $q$ is the charge on the particles and $r$ is the distance between them $(=2.5\times {10}^{-2}m).$
$\therefore \frac{1}{4\pi \epsilon o}\frac{q^2}{r^2}=0.036N$
$\Rightarrow 9\times {10}^9\times \frac{q^2}{2.5\times {10}^{-2}\times 2.5\times {10}^{-2}}=0.036N$
$\Rightarrow q=5\times {10}^{-8}C$