A particle of specific charge q / m=π C kg -1 is projected from the origin toward positive x-axis with a velocity of 10 m s -1 in a uniform magnetic field vecB=-2 hatk T. The velocity vecv of particle after time t=1 / 12 s will be (. in .m s -1)

Question

A particle of specific charge q / m=π C kg -1 is projected from the origin toward positive x-axis with a velocity of 10 m s -1 in a uniform magnetic field vecB=-2 hatk T. The velocity vecv of particle after time t=1 / 12 s will be (. in .m s -1) (A) 5[ hati+√3 hatj] (B) 5[√3 hati+ hatj] (C) 5[√3 hati- hatj] (D) 5[ hati+ hatj]

Tardigrade Admin · Accepted Answer

Time period, T=(2 π m/q B)=(2 π/π × 2)=1 s <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/3c399ed282ce0dcfcb612c765c8844fe-.png" /> Thus, particle will be at point P after t=(1/12) s vecv=10[ cos 30 hati+ sin 30 hatj] vecv=10[(√3/2) hati+(1/2) hatj]=5[√3 hati+ hatj] ms -1

Q. A particle of specific charge $q / m = π C k g^{- 1}$ is projected from the origin toward positive $x$ -axis with a velocity of $10 m s^{- 1}$ in a uniform magnetic field $B = - 2 \hat{k} T$ . The velocity $v$ of particle after time $t = 1/12 s$ will be $($ in $m s^{- 1})$

$5 [\hat{i} + 3 \hat{j}]$

$5 [3 \hat{i} + \hat{j}]$

$5 [3 \hat{i} - \hat{j}]$

$5 [\hat{i} + \hat{j}]$

Time period, $T = \frac{2 πm}{qB} = \frac{2 π}{π \times 2} = 1 s$

Thus, particle will be at point $P$ after $t = \frac{1}{12} s$
$v = 10 [cos 30 \hat{i} + sin 30 \hat{j}]$
$v = 10 [\frac{3}{2} \hat{i} + \frac{1}{2} \hat{j}] = 5 [3 \hat{i} + \hat{j}] m s^{- 1}$

Q. A particle of specific charge q/m=πCkg−1 is projected from the origin toward positive x-axis with a velocity of 10ms−1 in a uniform magnetic field B=−2k^T. The velocity v of particle after time t=1/12s will be ( in ms−1)

5[i^+3​j^​]

5[3​i^+j^​]

5[3​i^−j^​]

5[i^+j^​]