Question

Specific charges of two particles $A$ and $B$ are in ratio $2:3$,If their mass ratio $m_A:m_B$ is $2:3$, then find ratio of their charges $\left(\frac{q_A}{q_B}\right)?$

Answer 1

Given:

Ratio of mass, $\frac{m_A}{m_B}=\frac{2}{3}$

Ratio of specific charge of A and B$=\frac{2}{3}$

Let the specific charge of particle A be $Q_A$ and that of B is $Q_B$.

We know that:

Specific charge, $Q=\frac{charge}{mass}$

Thus,

$\frac{Q_A}{Q_B}=\frac{q_A}{m_A}\times \frac{m_B}{q_B}$

Putting the valueof $Q_A$ and $Q_B$ in the above equation;

$\frac{2}{3}=\frac{q_A}{q_B}\times \frac{3}{2}$

Therefore,

$\frac{q_A}{q_B}=\frac{4}{9}$

Thus, the ratio of the charges is $\frac{4}{9}$.