JEE Mains 2025 Physics: Magnetic Field at Centre of Square Loop | 8 April Shift 2 PYQ
This post provides a detailed step-by-step solution to an important JEE Mains 2025 Physics question from 8th April Shift 2. The topic involves calculating the resultant magnetic field at the center of a square loop with unequal resistance paths. This concept is crucial for JEE Mains 2026 and JEE Mains 2027 aspirants preparing for magnetostatics and current electricity.
Question
Figure shows a current-carrying square loop ABCD of edge length ‘a’ lying in a plane. If the resistance of the ABC part is r and that of the ADC part is 2r, then the magnitude of the resultant magnetic field at the center of the square loop is:
Options:
- (1) √2μ₀I / 3πa
- (2) μ₀I / 2πa
- (3) 2μ₀I / 3πa
- (4) 3πμ₀I / √2a
Given image-based question from JEE Mains 2025:
More JEE Mains 2025 Physics PYQ
Detailed Step-by-Step Solution
Step 1: Use Current Division Based on Resistance
Total current entering at point A is I. It splits into two paths:
- Path ABC with resistance r
- Path ADC with resistance 2r
Using the current division rule:
i₁ = (2r)/(r + 2r) × I = 2I/3 through ABC
i₂ = (r)/(r + 2r) × I = I/3 through ADC
Step 2: Magnetic Field at the Centre Due to One Side
For a current-carrying straight segment forming a square loop, the magnetic field at the center from one side is:
B = (μ₀i√2) / (2πa)
Step 3: Field Contribution from Path ABC (Current i₁)
Sides AB and BC both contribute field into the page. Their combined vector sum:
BABC = 2 × (μ₀i₁√2) / (2πa) = (μ₀√2 × 2I/3) / (πa)
Step 4: Field Contribution from Path ADC (Current i₂)
Sides AD and DC contribute field out of the page. Their combined field:
BADC = 2 × (μ₀i₂√2) / (2πa) = (μ₀√2 × I/3) / (πa)
Step 5: Net Magnetic Field at the Centre
Since the fields are in opposite directions:
Bnet = BABC – BADC = (μ₀√2I / 3πa)
✅ Final Answer: Option (1) √2μ₀I / 3πa
Watch the Full Video Solution
Watch the full explanation and visual walkthrough of this question:
Conclusion
This problem highlights the application of current division and vector addition of magnetic fields from wire segments. Mastering such conceptual questions is vital for scoring high in JEE Mains Physics.
