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QJEEM23Ph6b18: JEE Main 2023 Physics - Class 12 JEEM23Ph6b18 Solution: As shown in the figure, a current of flowing in an equilateral…

As shown in the figure, a current of 2 A2 \mathrm{~A} flowing in an equilateral triangle of side 43 cm4 \sqrt{3} \mathrm{~cm} . The magnetic field at the centroid O\mathrm{O} of the triangle is

JEE Main 2023 (Online) 30th January Evening Shift Physics - Magnetic Effect of Current Question 68 English

(Neglect the effect of earth's magnetic field)

Multiple Choice Options

  • A 43×10−4 T4 \sqrt{3} \times 10^{-4} \mathrm{~T}
  • B 43×10−5 T4 \sqrt{3} \times 10^{-5} \mathrm{~T}
  • C 33×10−5 T3 \sqrt{3} \times 10^{-5} \mathrm{~T}
  • D 3×10−4 T\sqrt{3} \times 10^{-4} \mathrm{~T}

Step-by-Step Verified Solution

Bnet=μ0i4πr(sin⁡α+sin⁡β)×3{B_{net}} = {{{\mu _0}i} \over {4\pi r}}(\sin \alpha + \sin \beta ) \times 3

=μ0×24π×(2×10−2)×(32+32)×3= {{{\mu _0} \times 2} \over {4\pi \times (2 \times {{10}^{ - 2}})}} \times \left( {{{\sqrt 3 } \over 2} + {{\sqrt 3 } \over 2}} \right) \times 3

=10−7×102(33)= {10^{ - 7}} \times {10^2}(3\sqrt 3 )

=33×10−5= 3\sqrt 3 \times {10^{ - 5}} T

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