First slide

current density

Question

A 1 µA beam of protons with a cross-sectional area of 0.5 sq. mm is moving with a velocity of $3 x 10^{4} {ms}^{- 1}$ . Then charge density of beam is

Moderate

A

$6.6 x 10^{- 4} C / m^{3}$
B

$6.6 x 10^{- 5} C / m^{3}$
C

$6.6 x 10^{- 6} C / m^{3}$
D

None of these

Solution

For one second, distance = Velocity = $3 \times 10^{- 4} m / \sec$
$\begin{array}{l} and Q = i \times 1 = 10^{- 6} C . Charge density = \frac{Charge}{Volume} \\ \frac{10^{- 6}}{3 \times 10^{4} \times 0 .5 \times 10^{- 6}} = 6 .6 \times 10^{- 5} C / m^{3} . \end{array}$

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