Question

A conductor carries a current $50\mu A$. If the area of cross-section of the conductor is $50m{m^2}$, then value of the current density in $A{m^{ - 2}}$ is
A) 0.5
B) 1
C) ${10^{ - 3}}$
D) ${10^{ - 6}}$

Answer 1

Hint:The question is from electricity. Substitute the value of current (I) and cross-section area (A) in the current density equation and find the value of current density (J).


Formula Used:
\[J = \dfrac{I}{A}\]
Where,
J = Current density
I = Current
A = Cross-section area


Complete answer:
Current density is defined as the total amount of current passing through a unit cross-sectional conductor in unit time. The equation for current density is given below.
\[J = \dfrac{I}{A}\]
Where,
J = Current density
I = Current
A = Cross-section area
The value of current and cross-section area is given. \[I = 50\mu A = 50 \times {10^{ - 6}}A\] and \[A = 50m{m^2} = 50 \times {10^{ - 6}}{m^2}\].
\[J = \dfrac{I}{A} = \dfrac{{50 \times {{10}^{ - 6}}}}{{50 \times {{10}^{ - 6}}}} = 1A{m^{ - 2}}\]

Hence, the correct option is Option B) 1.

Additional Information:
Drift velocity is the average velocity attained by charged particles, (electrons) in a material due to an electric field (\[\overrightarrow E \]). The SI unit of drift velocity is the same as velocity which is m/s. The drift velocity and current flowing through the conductor both increase as the intensity of the electric field increases. Drift velocity is directly proportional to current.
The relation between drift velocity and current is given below.
\[{v_d} = \dfrac{I}{{neA}}\]
\[{v_d}\]= drift velocity
I = current flow
n = free electron density
e = charge of an electron
A = cross sectional area
Mobility (\[\mu \]) of an electron is the drift velocity of an electron for a unit electric field (\[E\]). The equation for mobility is given below.
\[\mu = \dfrac{{{v_d}}}{E}\]



Note: The relation between drift velocity and Current Density is \[J = n{v_d}e\]. Where, n = free electron density, e = charge of an electron, \[{v_d}\]= drift velocity and J = current density.