Question

A double ionized He+2 atom travels at right angles lo a magnetic field of induction 0.4 T at a velocity of 10 m/s describing a circle of radius r. A proton travelling with the same speed in the same direction in the same field will describe a circle radius:

• A. $\frac{r}{4}$
• B. $\frac{r}{2}$
• C. $r$
• D. $2r$

Answer 1

Answer: (B)

The necessary centripetal force for circular path is provide by magnetic force $\frac{m{\mu }^2}{r}=qvB$ $r=\frac{mv}{qB}$ (Here: velocity is same i.e., $v_p=v_{He}$ and field is same $B_1=B_2,$ $m_{He}=4m_p,q_{{}_{He}}=2q_p$ ) $r\propto \frac{m}{q}$ Hence, $\frac{r_{He}}{r_p}=\frac{m_{He}}{m_p}\times \frac{q_p}{q_{He}}=\frac{4m_p}{m_p}\times \frac{q_p}{2q_p}$ $r_{He}:r_p=2:1$ Hence, $r_p:r_{He}=1:2$