Question

Two identical particles having same mass m and charges +q and -q separated by a distance 'd' enters in a uniform magnetic field B directed perpendicular to the plane of paper inward with speeds v1 and v2 as shown in the figure. The particle will not collide if:

Answer 1

Answer:

Option (2) $d > \frac{2m}{Bq}(v_1+v_2)$

Explanation:

When a charged particle moves in a magnetic field, it follows a circular path

The radius of the circular path is given by

$\boxed{r=\frac{mv}{Bq}}$

where m is the mass of the charge q, v is its velocity and B is the magnetic field

Since the magnetic field is perpendicular to the plane of the paper, the particle will follow the circular path in the plane of the paper

Particle with -q charge will move clockwise while the particle with q charge will move anticlockwise

If the radius of their paths are are r₁ and r₂ respectively

Then their diameters will be 2r₁ and 2r₂

The particles will not collide if

$d>2r_1+2r_2$

$\implies d > \frac{2mv_1}{Bq} +\frac{2mv_2}{qB}$

$\implies d > \frac{2m}{Bq}(v_1+v_2)$

Answer 2

Explanation:

hope this will help you ☺️