Question

A current 1.8 flows through a wire of area of cross sectional area 0.5 mm2. Find the the current density in the wire
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Answer 1

Answer:

$\boxed{\mathfrak{Current \ density \ (j) = 3.6 \times {10}^{6} \: A {m}^{ - 2}}}$

Given:

Current (I) = 1.8 A

Cross-section area = 0.5 mm² = $\sf 0.5 \times 10^{-6}$ m²

To Find:

Current density (j) in the wire

Explanation:

Formula of current density (j):

$\boxed{ \bold {j = \frac{I}{A}}}$

Substituting value of I & A in the formula:

$\sf \implies j = \frac{1.8}{0.5 \times {10}^{ - 6} } \\ \\ \sf \implies j = \frac{1.8}{0.5} \times {10}^{6} \\ \\ \sf \implies j = 3.6 \times {10}^{6} \: A {m}^{ - 2}$

$\therefore$

Current density (j) in the wire = $\sf 3.6 \times {10}^{6} \: A {m}^{ - 2}$

Answer 2

Answer

Current Density = 3.6 × 10⁶ A/m²

Given

A current 1.8 flows through a wire of area of cross sectional area 0.5 mm²

To Find

Current density

Formula Applied

Current Density is defined as the current passing through the unit cross-sectional area of the substance

$\bigstar\ \; \bold{j=\dfrac{I}{A}}$

where ,

• j denotes current density
• I denotes current
• A denotes cross-section area

Solution

Current , I = 1.8 A

Cross-sectional area of wire , A = 0.5 mm²

⇒ A = 0.5 × 10⁻⁶ m²

Current Density , j = ? A/m²

Apply formula ,

$\implies \rm j=\dfrac{I}{A}\\\\\implies \rm j=\dfrac{1.8}{0.5\times 10^{-6}}\\\\\implies \rm j=\dfrac{3.6}{10^{-6}}\\\\\implies \bf j=3.6\times 10^6\ A/m^2\ \; \orange{\bigstar}$

More Info

• SI unit of Current density , j is A/m²
• SI unit of Current , I is Ampere
• SI unit of Area , A is m²