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

Question

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" /> (A) qBv (B) (m v/q B) (C) qBd (D) (2 m v2/q B)

Tardigrade Admin · Accepted Answer

As d < < < (m v/q B) d=r sin θ Impulse is change in momentum Solution

sin θ =(d/r) where r=(m v/q B) ∴ d < < < r ∴ sin θ =θ θ =(d/r) Change in momentum =mv θ =mv × (d/r)=(m v × d × q B/m v) Impulse=qBd

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

$(d << \frac{m v}{qB})$

$qB v$

$\frac{m v}{qB}$

$qB d$

$\frac{2 m v ^{2}}{qB}$

As $d <<< \frac{m v}{qB}$
$d = r s in θ$
Impulse is change in momentum

$s in θ = \frac{d}{r}$
where $r = \frac{m v}{qB}$
$∴ d <<< r$
$∴ s in θ = θ$
$θ = \frac{d}{r}$
Change in momentum
$= m v θ$
$= m v \times \frac{d}{r} = \frac{m v \times d \times qB}{m v}$
$I m p u l se = qB d$

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 (d<<qBmv​)

qBv

qBmv​

qBd

qB2mv2​