Magnetic Field of a Current-Carrying Wire
Calculation Results:
Current (I): I (uniformly distributed)
Wire radius (a): a
Observation radius (r): a
Region: r = a
Current enclosed (Ienc): I
Magnetic field (B): μ₀I/(2πa)
Field direction: Circular around wire (right-hand rule)
Example Explanation
This simulation demonstrates Example 4.8 where we calculate the magnetic field both inside and outside a long straight wire with circular cross-section carrying steady current I.
Given:
- Wire radius: a
- Current: I (uniformly distributed)
- Observation point at distance r from center
Key steps:
- For r > a (outside the wire):
∮B·dl = μ₀Ienc ⇒ B(2πr) = μ₀I ⇒ B = μ₀I/(2πr)
- For r ≤ a (inside the wire):
Ienc = I(πr²)/(πa²) = I(r²/a²)
∮B·dl = μ₀Ienc ⇒ B(2πr) = μ₀I(r²/a²) ⇒ B = (μ₀Ir)/(2πa²)
Key observations:
- Field inside wire (r ≤ a) grows linearly with r: B ∝ r
- Field outside wire (r > a) falls off as 1/r: B ∝ 1/r
- Maximum field occurs at the surface (r = a): B = μ₀I/(2πa)
