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  4. A charged particle of mass m and charge q is projected into a uniform magnetic field of induction B with speed v which is perpendicular to B . The width of the magnetic field is d . The impulse imparted to the particle by the field is (d < < (m v/q B)) <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-xpilxv0hprpw.png />

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Q. A charged particle of mass $m$ and charge $q$ is projected into a uniform magnetic field of induction $B$ with speed $v$ which is perpendicular to $B$ . The width of the magnetic field is $d$ . The impulse imparted to the particle by the field is

$\left(d \, < < \, \frac{m v}{q B}\right)$

Question

NTA AbhyasNTA Abhyas 2020Moving Charges and Magnetism

Solution:


Solution
As $d \, < < < \, \frac{m v}{q B}$
$d=r \, sin \theta $
Impulse is change in momentum

Solution
$sin \theta =\frac{d}{r}$
where $r=\frac{m v}{q B}$
$\therefore \, d \, < < < \, r$
$\therefore sin \theta =\theta $
$\theta =\frac{d}{r}$
Change in momentum
$=mv \, \theta $
$=mv \, \times \, \frac{d}{r}=\frac{m v \times d \times q B}{m v}$
$Impulse=qBd$