A uniform magnetic field vecB=B0 hatj exists in space. A particle of mass m and charge q is projected towards negative x-axis with speed v from the a point (d, 0,0). If the maximum value of v for which the particle does not hit y-z plane is (4 B0 q d/α m), then calculate α.

Question

A uniform magnetic field vecB=B0 hatj exists in space. A particle of mass m and charge q is projected towards negative x-axis with speed v from the a point (d, 0,0). If the maximum value of v for which the particle does not hit y-z plane is (4 B0 q d/α m), then calculate α. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/acd83793071af075239c42caab8b81d3-.png" /> vecB=B0 hatj The particle will not hit y-z plane if radius of curvature r ≤ d ∴ (m v2/d)=q v B0 ⇒ v=(B0 q d/m)

Q. A uniform magnetic field B=B0​j^​ exists in space. A particle of mass m and charge q is projected towards negative x-axis with speed v from the a point (d,0,0). If the maximum value of v for which the particle does not hit y−z plane is αm4B0​qd​, then calculate α.

B=B0​j^​ The particle will not hit y−z plane if radius of curvature r≤d ∴dmv2​=qvB0​ ⇒v=mB0​qd​

$B = B_{0} \hat{j}$
The particle will not hit $y - z$ plane if radius of curvature
$r \leq d$
$∴ \frac{m v ^{2}}{d} = q v B_{0}$
$\Rightarrow v = \frac{B _{0} q d}{m}$