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  • Two straight infinitely long and thin parallel wires are held 0.1 m apart and carry a current of 5 A each in the same direction. The magnitude of the magnetic field at a point distant 0.1

Two straight infinitely long and thin parallel wires are held 0.1 m apart and carry a current of 5 A each in the same direction. The magnitude of the magnetic field at a point distant 0.1m from both wires is

Option: 1

10^{-5} \mathrm{~T}


Option: 2

\sqrt{2} \times 10^{-5} \mathrm{~T}


Option: 3

\sqrt{3} \times 10^{-5} \mathrm{~T}


Option: 4

2 \times 10^{-5} \mathrm{~T}


Answers (1)

best_answer

Wires A and B carry current I=5 A each coming out of the plane of the page as shown in the below figure.

The magnitude of magnetic field at point P due wire A is equal to that due to wire B, i.e.

\mathrm{B_A =B_B=\frac{\mu_0}{4 \pi} \cdot \frac{2 I}{a} \\ }

\mathrm{ =\frac{10^{-7} \times 2 \times 5}{0.1}=10^{-5} \mathrm{~T} }

The direction of field \mathrm{ B_A }  is perpendicular to \mathrm{ PA }  and that of field \mathrm{ B_B }  is perpendicular to \mathrm{ PB } . Therefore, the angle between the two fields is  \mathrm{\theta=60^{\circ} }  The magnitude of the resultant field at P is given by
\mathrm{ B_R^2=B_A^2+B_B^2+2 B_A B_B \cos \theta }
which gives  \mathrm{ B_R=2 B_A \cos \left(\frac{\theta}{2}\right) }

\mathrm{ =2 \times 10^{-5} \times \frac{\sqrt{3}}{2}=\sqrt{3} \times 10^{-5} \mathrm{~T} }

Hence the correct choice is (c).

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vinayak

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