Question

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An Aluminium wire of diameter 4 mm carries a current of 2.2 A. Then the current density is
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Answer 1

$\huge \fcolorbox{red}{pink}{Solution :)}$

Given ,

• Diameter = 4 mm or 4 × (10)^-3 m
• So , Radius = 2 × (10)^-3 m
• Current = 2.2 amp

We know that , the formula of current density is given by

$\large \mathtt{ \fbox{Current \: density = \frac{Current }{Area} }}$

Substitute the known values , we get

$\sf \hookrightarrow Curent \: density = \frac{ 2.2 \times 7 }{22 \times {(2 \times {(10)}^{ - 3}) }^{2} } \\ \\ \sf \hookrightarrow Curent \: density = \frac{7}{4 \times {(10)}^{ - 6} \times 10 } \\ \\ \sf \hookrightarrow Curent \: density = \frac{7}{4 \times {(10)}^{ - 5} } \\ \\ \sf \hookrightarrow Curent \: density = 1.75 \times {(10)}^{5} \: \: amp/ {m}^{2}$

Hence , the current density is 1.75 × (10)^5 amp/m²

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