A uniform magnetic field of magnitude $0.20 T$ exists in space from east to west. With what speed should a particle of mass $0.010 g$ and having a charge $1.0 \times 10^{- 5} C$ be projected from south to north so that it moves with a uniform velocity?

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Solution

For uniform velocity, gravitational force acting on mass must be balanced by a magnetic force
$F_{g} = m g$
$F_{B} = q v B$
$F_{g} = F_{B}$
$m g = q v B$

$v = \frac{m g}{q B}$

$v = \frac{0.01 \times 10^{- 3} \times 10}{1 \times 10^{- 5} \times 0.2}$

$v = 50 m / s e c$

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A uniform magnetic field of magnitude 0.20 T exists in space from east to west. With what speed should a particle of mass 0.010 g and having a charge 1.0×10−5C be projected from south to north so that it moves with a uniform velocity?

For uniform velocity, gravitational force acting on mass must be balanced by a magnetic forceFg=mgFB=qvBFg=FB mg=qvBv=mgqBv=0.01×10−3×101×10−5×0.2v=50m/sec

A uniform magnetic field of magnitude $0.20 T$ exists in space from east to west. With what speed should a particle of mass $0.010 g$ and having a charge $1.0 \times 10^{- 5} C$ be projected from south to north so that it moves with a uniform velocity?

For uniform velocity, gravitational force acting on mass must be balanced by a magnetic force
$F_{g} = m g$
$F_{B} = q v B$
$F_{g} = F_{B}$
$m g = q v B$

$v = \frac{m g}{q B}$

$v = \frac{0.01 \times 10^{- 3} \times 10}{1 \times 10^{- 5} \times 0.2}$

$v = 50 m / s e c$