Question

A proton, deutron and an $\alpha$-particle enter a magnetic field perpendicular to field with same velocity. What is the ratio of the radii of circular paths?

• A. 1 : 2 : 2
• B. 2 : 1 : 1
• C. 1 : 1 : 2
• D. 1 : 2 : 1

Answer 1

Answer: (A)

$\text{Force on a charged particle due circular motion:}F=\frac{m{v}^2}{r}$

$\text{Force on a charged particle due to magnetic field:}{F}_B=qvB$

$F=F_B\Rightarrow \frac{m{v}^2}{r}=qvB\Rightarrow r=\frac{mv}{qB}$

$\text{Here}v\text{and}\text{are constant.}$

$\Rightarrow r\propto \frac{m}{q}$

$\text{For proton:}{r}_p=1\times k$

$\text{For deutron:}{r}_d=2k$

$\text{For an-}\alpha \text{particle:}{r}_{\alpha }=2k$

$\text{Therefore,}{r}_p:r_d:r_{\alpha }=1:2:2$