Current Electricity – Stage 1 (Concept Building)

Page 4: Current Density & Its Relation with Drift Velocity

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1️⃣ What is Current Density?

Current Density is defined as the electric current flowing per unit cross-sectional area of a conductor.

Definition:
J = I / A

• J → Current density
• I → Current (Ampere)
• A → Area (m²)

SI Unit: Ampere per square meter (A/m²)

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2️⃣ Vector Nature of Current Density

Current density is a vector quantity.

• Direction of J is same as conventional current
• Magnitude depends on current and area

⚠️ JEE Trap:
Current is scalar, but current density is vector.

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3️⃣ Microscopic Expression of Current Density

From microscopic theory of conduction:

Key Relation:
J = nqv_d

• n → Number density of free electrons
• q → Charge of electron
• v_d → Drift velocity

This formula connects microscopic motion with macroscopic current.

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4️⃣ Relation Between J and I

Using:

• I = nqAv_d
• J = I / A

Hence:
J = nqv_d

Area cancels out → current density depends only on material properties.

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5️⃣ Physical Meaning (Very Important for JEE)

• High current density → more charge flow per unit area
• Thin wires have higher current density for same current
• Heating effects depend on current density

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6️⃣ Comparison: Current vs Current Density

Current (I)	Current Density (J)
Scalar quantity	Vector quantity
Depends on total charge flow	Depends on area also
Unit: Ampere	Unit: A/m²

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7️⃣ JEE Concept Checks

• Same current in thick and thin wire → different J
• Higher J → more heating
• J is maximum at narrow sections

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8️⃣ Foundation Insight

IIT Thinking:
Current density tells how “crowded” moving charges are inside a