As shown in the figure, a current of 2,A flowing in an equilateral triangle of side 4 3,cm. The magnetic field at the centroid O of the triangle is: (Neglect the effect of earth's magnetic field.)

(A) 4 \sqrt{3} \times 10^{-4} \,T

(B) 4 \sqrt{3} \times 10^{-5} \,T

(C) \sqrt{3} \times 10^{-4}\, T

JEE Mains · Physics · STD 12 - Moving charges and magnetism

As shown in the figure, a current of \(2\,A\) flowing in an equilateral triangle of side \(4 \sqrt{3}\,cm\). The magnetic field at the centroid \(O\) of the triangle is: (Neglect the effect of earth's magnetic field.)

Pick an option to check your answer.

Verified Solution

Correct Answer

(D) \(3 \sqrt{3} \times 10^{-5}\,T\)

Detailed explanation

\(d \tan 60^{\circ}=2 \sqrt{3}\)

\(d =2\,cm\)

\(B =3 \times \frac{\mu_0 i }{2 \pi d } \sin 60^{\circ}\)

\(=3 \times \frac{2 \times 10^{-7} \times 2}{2 \times 10^{-2}} \times \frac{\sqrt{3}}{2}\) \(=3 \sqrt{3} \times 10^{-5}\)

Same subject

List \(I\)	List \(II\)
\(A\) Troposphere	\(I\) Approximate \(\quad 65-75\, km\) over Earth's surface
\(B\) E-Part of Stratosphere	\(II\) Approximate \(300\,km\) over Earth's surface
\(C\) \(F _2\)-Part of Thermosphere	\(III\) Approximate \(10\,km\) over Earth's surface
\(D\) \(F _2\)-Part of Thermosphere	\(IV\) Approximate \(100\,km\) over Earth's surface

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