A magnetic field of $4 \times 10^{- 3} \hat{K} T$ exerts a force of $(4 \hat{i} + 3 \hat{j}) \times 10^{- 10} N$ on a particle of charge $10^{- 9} C$ and going in X-Y plane. The velocity of the charged particle is

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

75 \hat{i} - 100 \hat{J}

- 75 \hat{i} + 100 \hat{J}

100 \hat{i} - 75 \hat{J}

100 \hat{i} + 75 \hat{J}

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

\vec{F} = q (\vec{V} \times \vec{B})

$let \vec{V} = (x \hat{i} + y \hat{j}) {ms}^{- 1}$

$(4 \hat{i} + 3 \hat{j}) \times 10^{- 10} = 10^{- 9} (x \hat{i} + y \hat{j}) \times 4 \times 10^{- 3} \hat{k}$

$(4 \hat{i} + 3 \hat{j}) = \frac{10^{- 9}}{10^{- 10}} (- x \hat{i} + y \hat{j}) \times 4 \times 10^{- 3}$

$4 \hat{i} + 3 \hat{j} = 4 \times 10^{- 2} (y \hat{i} - x \hat{j})$

$4 \hat{i} + 3 \hat{j} = \frac{4}{100} (y \hat{i} - x \hat{j})$

$100 \hat{i} + 75 \hat{j} = y \hat{i} - x \hat{j}$

$y = 100 and x = - 75$

$\vec{V} = (- 75 \hat{i} + 100 \hat{j}) {ms}^{- 1}$

Watch 3-min video & get full concept clarity