Question

A proton and an $\alpha$-particle, moving with the same velocity, enter a uniform magnetic field, acting normal to the plane of their motion. The ratio of the radii of the circular paths described by the proton and $\alpha$-particle is

• A. $1:2$
• B. $1:4$
• C. $4:1$
• D. $1:16$

Answer 1

Answer: (A)

$1:2$

When a charged particle enters a field, it takes a circular path. The radius of circular path is given by the relation

$r=\frac{mv}{Bq}$

For proton, $r_1=\frac{mv}{Bq}$

For $\alpha$-particle, $r_2=\frac{4m\times v}{B\times 2q}=\frac{2mv}{Bq}$

$\Rightarrow r_1:r_2::1:2$