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Question

Physics Question on Magnetic Field Due To A Current Element, Biot-Savart Law

As shown in the figure, a current of 2A2 A flowing in an equilateral triangle of side 43cm4 \sqrt{3} cm The magnetic field at the centroid OO of the triangle is
Magnetic field
(Neglect the effect of earth's magnetic field)

A

43×10−4T4 \sqrt{3} \times 10^{-4} T

B

3×10−4T\sqrt{3} \times 10^{-4} T

C

43×10−5T4 \sqrt{3} \times 10^{-5} T

D

33×10−5T3 \sqrt{3} \times 10^{-5} T

Answer

33×10−5T3 \sqrt{3} \times 10^{-5} T

Explanation

Solution

The correct answer is (D) : 33×10−5T3\sqrt3 \times10^{-5}T
d tan⁡60°=23d\ \tan60°=2\sqrt3
d = 2cm
B=3×μ0i2πdsin⁡60°B=3\times\frac{\mu_0i}{2\pi d}\sin60°
=3×2×10−7×22×10−2×32=3\times\frac{2\times10^{-7}\times2}{2\times10^{-2}}\times\frac{\sqrt3}{2}
=33×10−5=3\sqrt3\times10^{-5}