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Analysis of Force Equation

A charged par...

Question

A charged particle of mass $10^{- 3}$ kg and charge $10^{- 5} C$ enters a magnetic field of induction 1 T. If $g = 10 m s^{- 2}$ for what value of velocity will it pass straight through the field without deflection?

10^{- 3} m s^{- 1}

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10^{3} m s^{- 1}

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10^{6} m s^{- 1}

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1 m s^{- 1}

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Solution

The correct option is A $10^{3} m s^{- 1}$
Since the charged particle passes without being deflected,

$F_{m a g n e t i c} = F_{g r a v i t y}$

$∴ q v B = m g$

$∴ v = \frac{m g}{q B}$
$= \frac{10^{- 3} \times 10}{10^{- 5} \times 1} = 10^{3} m / s$

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