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NEET PHYSICSMOVING CHARGES AND MAGNETISMMedium

Question

A thick current-carrying cable of radius 'R' carries current 'I' uniformly distributed across its cross-section. The variation of magnetic field B(r) due to the cable with the distance 'r' from the axis of the cable is represented by:

A

Graph showing B linearly increasing for r < R and decreasing as 1/r for r > R

B

Graph showing B constant for r < R and decreasing for r > R

C

Graph showing B zero for r < R and decreasing for r > R

D

Graph showing B increasing parabolically for r < R and decreasing for r > R

Step-by-Step Solution

  1. Region 1: Inside the cable (r<Rr < R): Apply Ampere's Circuital Law: ∮B⋅dl=μ0Ienclosed\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enclosed}. For a path of radius rr inside the wire, the current enclosed is a fraction of the total current II, proportional to the area: Ienclosed=I(πr2πR2)=Ir2R2I_{enclosed} = I \left(\frac{\pi r^2}{\pi R^2}\right) = I \frac{r^2}{R^2} B(2πr)=μ0Ir2R2B(2\pi r) = \mu_0 I \frac{r^2}{R^2} B=(μ0I2πR2)rB = \left(\frac{\mu_0 I}{2\pi R^2}\right) r Thus, B∝rB \propto r (Linear increase passing through the origin).
  2. Region 2: Outside the cable (r≥Rr \geq R): The enclosed current is the total current II. B(2πr)=μ0IB(2\pi r) = \mu_0 I B=μ0I2πrB = \frac{\mu_0 I}{2\pi r} Thus, B∝1rB \propto \frac{1}{r} (Rectangular hyperbola decrease).
  3. Conclusion: The magnetic field increases linearly from zero at the axis to a maximum at the surface (r=Rr=R), and then decreases inversely with distance outside. This corresponds to the standard graph for a solid cylindrical wire .

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from MOVING CHARGES AND MAGNETISM. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSMOVING CHARGES AND MAGNETISMcurrentcarryingradiuscarriescurrentuniformly

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