A proton and an alpha particle moving with energies in the ratio $1: 4$ enter a uniform magnetic field of $3 T$ at right angles to the direction of magnetic field. The ratio of the magnetic forces acting on the proton and the alpha particle is

Question

Aicharya · Accepted Answer

$\frac{E_1}{E_2}=\frac{1}{4} \Rightarrow \frac{\frac{1}{2} m_1 v_1^2}{\frac{1}{2} m_2 v_2^2}=\frac{1}{4} \Rightarrow\left(\frac{1}{4}\right)\left(\frac{v_1}{v_2}\right)^2=\frac{1}{4}$ $\therefore \quad \mathrm{v}_1=\mathrm{v}_2$
$\therefore \quad$ Ratio of force, $\frac{F_1}{F_2}=\frac{B q_1 v_1}{B q_2 v_2}=\frac{q_1}{q_2}=\frac{1}{2}$

A proton and an alpha particle moving with energies in the ratio $1: 4$ enter a uniform magnetic field of $3…

Solution