Question

Two identical particles having the same mass m and charges +q and - q separated by a distance d enter in a uniform magnetic field B directed perpendicular to paper inwards with speed $v_1\text{and}{v}_2$ as shown in figure. The particles will not collide if

• A. $d>\frac{m}{Bq}(v_1+v_2)$
• B. $d<\frac{m}{Bq}(v_1+v_2)$
• C. $d>\frac{2m}{Bq}(v_1+v_2)$
• D. none of these

Answer 1

Answer: (A)

$d>\frac{m}{Bq}(v_1+v_2)$

Given : Two identical particles having the same mass m and charges +q and - q separated by a distance d enter in a uniform magnetic field B directed perpendicular to paper inwards with speed V1 and V2.

Solution :

Formula for radius of circular path of particle due moving inside magnetic field is $R=\frac{mv}{qB}$

$R_1=\frac{m{v}_1}{qB}$ , $R_2=\frac{m{v}_2}{qB}$

Force on moving charge $F=q(\overrightarrow{V}\times \overrightarrow{B})$

From this we can tell direction of force on the particles

Particle with negative charge will move downwards and with positive charge will move upward in the given case.

For particles to not collide d > $R_1+R_2$

d > $\frac{m{v}_1}{qB}$ + $\frac{m{v}_2}{qB}$

d >$\frac{m}{qB}(v1+v2)$

The correct opt :A