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Physics · 2024 · 3 marks
CBSE 2024 · Region 1 · Set 1 · Q23
(a) Define 'current density'. Is it a scalar or a vector? An electric field E is maintained in a metallic conductor. If n be the number of electrons…
Define 'current density'. Is it a scalar or a vector ? An electric field $\displaystyle \overrightarrow{\mathrm{E}}$ is maintained in a metallic conductor. If n be the number of electrons (mass m , charge -e ) per unit volume in the conductor and $\displaystyle \tau$ its relaxation time, show that the current density $\displaystyle \vec{j}=\alpha \vec{\mathrm{E}}$, where $\displaystyle \alpha=\left(\frac{\mathrm{ne}^{2}}{\mathrm{~m}}\right) \tau$.
What is a Wheatstone bridge ? Obtain the necessary conditions under which the Wheatstone bridge is balanced.
Marking-scheme solution
(a)
Current density is the amount of charge flowing per second per unit area normal to the flow.
Alternatively:
\[j=\frac{\mathrm{I}}{\mathrm{~A}}
\]
It is a vector quantity.
The amount of charge crossing the area A in time \(\displaystyle \Delta \mathrm{t}\) is \(\displaystyle \mathrm{I} \Delta \mathrm{t}\), where I is the magnitude of the current. Hence,
\[\mathrm{I} \Delta \mathrm{t}=\mathrm{ne} \mathrm{~A}\left|\mathrm{v}_{\mathrm{d}}\right| \Delta \mathrm{t}
\]
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