Two particles A and B of masses m and 2m have charges q and 2q respectively. Both particles moving with velocities upsilon 1 and upsilon 2 respectively in the same direction and enter the same magnetic field B acting normally to their direction of motion. If the two forces FA and FB acting on them are in the ratio of 1:2, the ratio of their velocities is

Question

Two particles A and B of masses m and 2m have charges q and 2q respectively. Both particles moving with velocities upsilon 1 and upsilon 2 respectively in the same direction and enter the same magnetic field B acting normally to their direction of motion. If the two forces FA and FB acting on them are in the ratio of 1:2, the ratio of their velocities is (A)  2:1  (B)  3:2  (C)  2:3  (D)  1:1

Tardigrade Admin · Accepted Answer

The magnetic Lorentz force acts on charge particle given by F=qvB text sinθ (FA/FB)=(q1v1B sin 90° /q2v2B sin 90° ) Or 1/2=(q/2q)(v1/v2) ∴ (v1/v2)=1/1

$2 : 1$

$3 : 2$

$2 : 3$

$1 : 1$

The magnetic Lorentz force acts on charge particle given by $F = q v B s in θ$ $\frac{F _{A}}{F _{B}} = \frac{q _{1} v _{1} B s i n 90 ^{\circ}}{q _{2} v _{2} B s i n 90 ^{\circ}}$ Or $1/2 = (q /2 q) (v_{1} / v_{2})$ $∴$ $\frac{v _{1}}{v _{2}} = 1/1$

2:1

3:2

2:3

1:1

The magnetic Lorentz force acts on charge particle given by F=qvBsinθ FB​FA​​=q2​v2​Bsin90∘q1​v1​Bsin90∘​ Or 1/2=(q/2q)(v1​/v2​) ∴ v2​v1​​=1/1

$2 : 1$

$3 : 2$

$2 : 3$

$1 : 1$

The magnetic Lorentz force acts on charge particle given by $F = q v B s in θ$ $\frac{F _{A}}{F _{B}} = \frac{q _{1} v _{1} B s i n 90 ^{\circ}}{q _{2} v _{2} B s i n 90 ^{\circ}}$ Or $1/2 = (q /2 q) (v_{1} / v_{2})$ $∴$ $\frac{v _{1}}{v _{2}} = 1/1$