Two charged particles A and B having the same charge, mass and speed enter into a magnetic field in such a way that the initial path of A makes an angle of 30° and that of B makes an angle of 90° with the field. Then the trajectory of

Question

Two charged particles A and B having the same charge, mass and speed enter into a magnetic field in such a way that the initial path of A makes an angle of 30° and that of B makes an angle of 90° with the field. Then the trajectory of (A) B will have smaller radius of curvature than that of A (B) both will have the same curvature (C) A will have smaller radius of curvature than that of B (D) both will move along the direction of their original velocities.

Tardigrade Admin · Accepted Answer

use qvB sin θ=(m v2/r) r propto (1/ sin θ) for the same values of m, v, q and B ∴ (rA/rB)=( sin 90°/ sin 30°)=2 or rA=2 rB or rB< rA

Q. Two charged particles $A$ and $B$ having the same charge, mass and speed enter into a magnetic field in such a way that the initial path of $A$ makes an angle of $3 0^{\circ}$ and that of $B$ makes an angle of $9 0^{\circ}$ with the field. Then the trajectory of

$B$ will have smaller radius of curvature than that of $A$

both will have the same curvature

$A$ will have smaller radius of curvature than that of $B$

both will move along the direction of their original velocities.

use $q v B sin θ = \frac{m v ^{2}}{r}$
$r \propto \frac{1}{s i n θ}$ for the same values of $m, v, q$ and $B$
$∴ \frac{r _{A}}{r _{B}} = \frac{s i n 9 0 ^{\circ}}{s i n 3 0 ^{\circ}} = 2$
or $r_{A} = 2 r_{B}$ or $r_{B} < r_{A}$

Q. Two charged particles A and B having the same charge, mass and speed enter into a magnetic field in such a way that the initial path of A makes an angle of 30∘ and that of B makes an angle of 90∘ with the field. Then the trajectory of

B will have smaller radius of curvature than that of A