Question

two particles A and B of masses m and 2m have charges q and 2q respectively. both these particles moving with vel. v1 and v2 reapectively in the same direction enter the same magnetuc field B acting normally to their direction of motion. if two forces Fa and Fb acting on them are in ratio 1:2, find the ratio of their velocities.

Answer 1

Magnetic force = B×V×Q. SO HERE B is constant velocity depends only on the ratio of force and charge, since the correct answer is 1:1

Answer 2

Answer: The correct answer is $\frac{v_{1}}{v_{2}}=\frac{1}{1}$.

Explanation:

The expression for Lorentz force is as follows;

$F=qvBsin\Theta$

Here, F is the force, q is the charge, v is the velocity, B is the magnetic field and $\Theta$ is the angle between velocity and the magnetic field.

The expression for Lorentz force for the particle A is as follows;

$F_{a}=q_{1}v_{1}Bsin\Theta$                                            ........ (1)

The expression for Lorentz force for the particle B is as follows;

$F_{b}=q_{2}v_{2}Bsin\Theta$                                          ......... (2)

Calculate the ratio of the velocities of the particles.

$\frac{F_{a}}{F_{b}}=\frac{q_{1}v_{1}Bsin\Theta}{q_{2}v_{2}Bsin\Theta}$

Put $\frac{F_{a}}{F_{b}}=\frac{1}{2}$, $q_{2}=q$ and $q_{2}=2q$

$\frac{1}{2}=\frac{qv_{1}Bsin\Theta}{2qv_{2}Bsin\Theta}$

$\frac{v_{1}}{v_{2}}=\frac{1}{1}$

Therefore, the ratio of their velocities is $\frac{v_{1}}{v_{2}}=\frac{1}{1}$.