Question

Two positively charged particles, one twice as massive as the other, are moving in the same circular orbit in a magnetic field. Which law explains to us why the less massive particle moves at twice the speed of the more massive particle?

• A. Coulomb's Law
• B. Conservation of angular momentum
• C. Hooke's Law
• D. The ideal gas law
• E. Heisenberg's uncertainty principle

Answer 1

The correct option is B Conservation of angular momentum

As there is no external torque on the given system of charges , therefore total angular momentum $L$ of the system remains constant according to law of Conservation of angular momentum i.e. ,

$L=I_1{\omega }_1+I_2{\omega }_2$ , ................$eq1$

where $I_1=m_1{r}^2$ (moment of inertia of first particle )

$I_2=m_2{r}^2$ (moment of inertia of second particle )

let first particle is massive than second, given that the mass of first particle is twice of the second,

$m_1=2m_2$

therefore $I_1=2I_2$ ,

if we use this relation in $eq1$, we can see that ,that the value of $L$ will be constant only when

${\omega }_2=2{\omega }_1$ ,

or $v_2=2v_1$ (given , $r$ is same for both particle)