Magnetic Field of a Cylindrical Conductor – Rankers Physics
Topic: Magnetic Effects of Current
Subtopic: Magnetic Field Due to Straight Current Carrying Wire

Magnetic Field of a Cylindrical Conductor

Assertion (A): The magnetic field induction due to an infinite long current carrying solid cylindrical conductor of radius \(R\), at a distance \(R/2\) and \(2R\) from its axis is same.
Reason (R): An infinite long current carrying solid cylindrical conductor is a source of uniform magnetic field.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is true: Using Ampere's Law, \(B(R/2) = \frac{\mu_0 I (R/2)}{2\pi R^2} = \frac{\mu_0 I}{4\pi R}\) and \(B(2R) = \frac{\mu_0 I}{2\pi (2R)} = \frac{\mu_0 I}{4\pi R}\).

Reason (R) is false: The magnetic field is not uniform; it varies linearly inside (\(B \propto r\)) and inversely outside (\(B \propto 1/r\)). Thus, A is true and R is false.

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