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NEET PHYSICSMOVING CHARGES AND MAGNETISMMedium

Question

A straight conductor carrying current II splits into two parts as shown in the figure. The radius of the circular loop is RR. The total magnetic field at the centre PP of the loop is:

A

Zero

B

3μ0i32R,inward\frac{3\mu_0 i}{32R}, \text{inward}

C

3μ0i32R,outward\frac{3\mu_0 i}{32R}, \text{outward}

D

μ0i2R,inward\frac{\mu_0 i}{2R}, \text{inward}

Step-by-Step Solution

  1. Concept: The problem involves determining the net magnetic field at the center of a circular loop where the current splits into two parallel paths (arcs). The two arcs have lengths l1l_1 and l2l_2 and carry currents I1I_1 and I2I_2 respectively.
  2. Current Division: Since the two arcs are connected in parallel, the potential difference (VV) across them is the same. According to Ohm's Law, V=I1R1=I2R2V = I_1 R_1 = I_2 R_2. Since resistance RR is proportional to length ll for a uniform wire (R=ρl/AR = \rho l/A), we have I1l1=I2l2I_1 l_1 = I_2 l_2 .
  3. Magnetic Field Calculation: The magnitude of the magnetic field BB at the center of a circular arc of length ll radius RR is given by the Biot-Savart Law as B=μ0Il4πR2B = \frac{\mu_0 I l}{4\pi R^2} .
  • Field due to arc 1: B1=μ0I1l14πR2B_1 = \frac{\mu_0 I_1 l_1}{4\pi R^2}
  • Field due to arc 2: B2=μ0I2l24πR2B_2 = \frac{\mu_0 I_2 l_2}{4\pi R^2}
  1. Superposition: The currents in the two arcs flow in opposite senses (one clockwise, the other counter-clockwise). Therefore, their magnetic fields at the center are directed in opposite directions (one inward, one outward). Since I1l1=I2l2I_1 l_1 = I_2 l_2, the magnitudes B1B_1 and B2B_2 are equal. Bnet=B1−B2=0B_{net} = B_1 - B_2 = 0

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 MAGNETISMstraightconductorcarryingcurrentsplits

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