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A uniform current I is flowing in a long...

A uniform current `I` is flowing in a long wire of radius `R`. If the current is uniformly distributed across the cross-sectional area of the wire, then

A

magnetic field increases linearly from centre to surface

B

magnetic field decays inversely with distance `r` from the centre of wire for `r gt R`

C

magnetic field at the centre of wire is zero

D

None of the above

Text Solution

AI Generated Solution

To solve the problem regarding the magnetic field due to a uniform current flowing in a long wire of radius \( R \), we can follow these steps: ### Step 1: Understand the Problem We have a long cylindrical wire with radius \( R \) carrying a uniform current \( I \). The current is uniformly distributed across the cross-sectional area of the wire. We need to analyze the magnetic field both inside and outside the wire. ### Step 2: Apply Ampere's Circuital Law Ampere's Circuital Law states that the line integral of the magnetic field \( \mathbf{B} \) around a closed loop is equal to the permeability of free space \( \mu_0 \) times the total current \( I_{\text{enc}} \) enclosed by the loop: \[ ...
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