A magnetic field of (4×10-3 hatk) T exerts a force of (4 hati+3 hatj)×10-10N on a particle having charge of 1×10-9C and moving in x-y plane. Find the velocity of the particle.

Question

A magnetic field of (4×10-3 hatk) T exerts a force of (4 hati+3 hatj)×10-10N on a particle having charge of 1×10-9C and moving in x-y plane. Find the velocity of the particle. (A) (75 hati+100 hatj) ms-1 (B) (75 hati-100 hatj) ms-1 (C) (-75 hati+100 hatj) ms-1 (D) (-75 hati-100 hatj) ms-1

Tardigrade Admin · Accepted Answer

As F = q(v × B) ∴ (4 hati + 3 hatj) × 10-10 = 10-9[(vx hati + vy hatj) × ( 4 × 10-3 hatk)] Solving, vx = - 75 m/s and vy = 100 ms-1 ∴ Required velocity is (- 75i + 100j) ms-1 .

Q. A magnetic field of $(4 \times 1 0^{- 3} \hat{k}) T$ exerts a force of $(4 \hat{i} + 3 \hat{j}) \times 1 0^{- 10} N$ on a particle having charge of $1 \times 1 0^{- 9} C$ and moving in x-y plane. Find the velocity of the particle.

$(75 \hat{i} + 100 \hat{j}) m s^{- 1}$

$(75 \hat{i} - 100 \hat{j}) m s^{- 1}$

$(- 75 \hat{i} + 100 \hat{j}) m s^{- 1}$

$(- 75 \hat{i} - 100 \hat{j}) m s^{- 1}$

As $F = q (v \times B)$
$∴$ $(4 \hat{i} + 3 \hat{j}) \times 1 0^{- 10} = 1 0^{- 9} [(v_{x} \hat{i} + v_{y} \hat{j}) \times (4 \times 1 0^{- 3} \hat{k})]$
Solving, $v_{x}$ = - 75 m/s and $v_{y}$ = 100 $m s^{- 1}$
$∴$ Required velocity is $(- 75 i + 100 j) m s^{- 1}$ .

Q. A magnetic field of (4×10−3k^)T exerts a force of (4i^+3j^​)×10−10N on a particle having charge of 1×10−9C and moving in x-y plane. Find the velocity of the particle.

(75i^+100j^​)ms−1

(75i^−100j^​)ms−1

(−75i^+100j^​)ms−1

(−75i^−100j^​)ms−1