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NEET PHYSICSMOVING CHARGES AND MAGNETISMMedium

Question

A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field B with the distance d from the centre of the conductor is correctly represented by the figure:

A

Graph 1

B

Graph 2

C

Graph 3

D

Graph 4

Step-by-Step Solution

  1. Inside the Conductor (d<Rd < R): Using Ampere's Circuital Law for a solid cylindrical conductor carrying a uniform current II, the magnetic field BB at a distance dd inside is derived by considering the current enclosed by a loop of radius dd. The enclosed current is Iencl=I(d2/R2)I_{encl} = I(d^2/R^2). Applying ∮B⋅dl=μ0Iencl\oint B \cdot dl = \mu_0 I_{encl} yields B(2πd)=μ0I(d2/R2)B(2\pi d) = \mu_0 I (d^2/R^2), which simplifies to B=(μ0I2πR2)dB = \left(\frac{\mu_0 I}{2\pi R^2}\right)d. Thus, B∝dB \propto d (Linear increase) .
  2. Outside the Conductor (d>Rd > R): For points outside, the enclosed current is the total current II. Ampere's Law gives B(2πd)=μ0IB(2\pi d) = \mu_0 I, which simplifies to B=μ0I2πdB = \frac{\mu_0 I}{2\pi d}. Thus, B∝1dB \propto \frac{1}{d} (Hyperbolic decrease) .
  3. Graph Characteristics: The correct plot must show a straight line passing through the origin for d<Rd < R (linear rise) and a curve decreasing towards zero for d>Rd > R (rectangular hyperbola). This corresponds to Figure 4.14 in the NCERT text .

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 MAGNETISMcylindricalconductorradiuscarryingconstant

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