Conduction current density is related to electric field by the point form of Ohm’s law: J = σE = E/ρ. With E = 5 and resistivity ρ = 4.5, the current density is 5/4.5 ≈ 1.11 in the corresponding current-density units.
Formula / Key Relation
σ = 1/ρ
J = σE = E/ρ
J = 5/4.5 ≈ 1.11
Detailed Explanation
Concept & ReasoningResistivity tells us how strongly a material opposes conduction. Conductivity is its reciprocal, σ = 1/ρ. Therefore a finite electric field produces a conduction current density J = σE. The correct numerical value follows directly from dividing the field intensity by resistivity; multiplying E by ρ would reverse the physical relationship.How to Solve It in the ExamRemember: resistivity in denominator, conductivity in numerator.Important Exam PointDo a dimensional/physical sense check: larger resistivity must reduce J for the same E.Related Revision PathThis question sits in the revision path Electromagnetic Fields → Conduction and Current Density → Point Form of Ohm's…
Concept & Reasoning
Resistivity tells us how strongly a material opposes conduction. Conductivity is its reciprocal, σ = 1/ρ. Therefore a finite electric field produces a conduction current density J = σE. The correct numerical value follows directly from dividing the field intensity by resistivity; multiplying E by ρ would reverse the physical relationship.
How to Solve It in the Exam
Remember: resistivity in denominator, conductivity in numerator.
Important Exam Point
Do a dimensional/physical sense check: larger resistivity must reduce J for the same E.
Related Revision Path
This question sits in the revision path Electromagnetic Fields → Conduction and Current Density → Point Form of Ohm's Law .
Quick Trick
Remember: resistivity in denominator, conductivity in numerator.
Common Mistake
Using J = ρE instead of J = E/ρ.
Exam Tip
Do a dimensional/physical sense check: larger resistivity must reduce J for the same E.
SEO + Knowledge GraphRelated PYQs & Exam ContextExam path, knowledge path and deeper practice links.
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