Question

The current density at a point in a uniform copper wire of area 2.5mm*2 carrying a current of 1nA​

Answer 1

$\maltese \: \underline{ \underline{ \textsf{\textbf{AnsWer:}}}} \: \maltese$

Current Density :

• Current per unit area is called as current density.

Representation:

• Current = I
• Current Density = J
• Area = A

Conversion:

• A = 2.5 mm² = 2.5 × 10⁻⁶ m²
• I = 1 nA = 1 × 10⁻⁹ A

Calculation:

$\implies \rm J = \dfrac{I}{A}$

$\implies \rm J = \dfrac{1 \times {10}^{ - 9} }{2.5 \times {10}^{ - 6} }$

$\implies \rm J = \dfrac{1 \times {10}^{ - 9} \times {10}^{6} }{2.5 }$

$\implies \rm J = \dfrac{1 \times {10}^{ - 3} }{2.5 }$

$\implies \rm J = \dfrac{1 \times {10}^{ - 3} }{25 \times {10}^{ - 1} }$

$\implies \rm J = \dfrac{1 \times {10}^{ - 3} \times {10}^{1} }{25 }$

$\implies \rm J = \dfrac{1 \times {10}^{ - 2} }{25 }$

$\implies \rm J = 0.04 \times {10}^{ - 2}$

$\implies \rm J = 4 \times \times {10}^{ - 2} \times {10}^{ - 2}$

$\implies \underline{ \boxed{ \orange{\bf J = 4 \times {10}^{ - 4} \: A m^{-2}}}}$

Hence, option A) is the correct answer.