Question

A doubly ionized $H{e}^{+2}$ atom travels at right angles to a magnetic field of induction $0.4T$ at a velocity of ${10}^{5}m/s$ describing a circle of radius $r$. A proton traveling with same speed in the same direction in the same field will describe a circle of radius :

• A. $0.25r$
• B. $0.5r$
• C. $r$
• D. $2r$

Answer 1

Answer: (B)

$0.5r$

Force on $H{e}^{+2}$ towards the center,
given, $2e\times {10}^5\times B=\frac{m{v}^2}{r}$
$r=\frac{4pv}{2e\times B}$-------(1)
where mass of $H{e}^{+2}$ is 4 times that of proton .
where p is mass of proton and e is charge on electron.
In 2nd case, according to question, radius $\left(r_1\right)=\frac{mv}{qB}$
$\Rightarrow r_1=\frac{pv}{eB}$ [ from (1)]
$\Rightarrow r_1=\frac{r}{2}$