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Two long parallel wires p and c_p are both perspendicular to the plane of the paper with distance of 5m between them. If p and c_pcarry currents of 2.5 amp and 5 amp respectively in the same direction, then the magnetic field at a point half way between the wires is -

Option: 1

\frac{3 \mu_0}{2 \pi}


Option: 2

\frac{\mu_0}{\pi}


Option: 3

\frac{\sqrt3 \mu_0}{2 \pi}


Option: 4

\frac{ \mu_0}{2 \pi}


Answers (1)

best_answer

When the current flows in both wires in the same direction then magnetic field at half way due to the wire p,

\overrightarrow{B_p}=\frac{\mu_0 I_1}{2 \pi S_2}=\frac{\mu_0 I_1}{5 \pi}=\frac{\mu_0}{2 \pi}\ \ \ \text (where I_1=2.5 \mathrm{Amp})

The direction of \overrightarrow{B_p} in downward \odot

Magnetic field at half way due to wire is

\vec{B}_G=\frac{\mu_0 I_2}{2 \pi 5 / 2}=\frac{\mu_0}{\pi}\ \ \text { (upward } \otimes)                (where I_2 = 2.5 amp)

Net magnetuc field at half way

\vec{B}=\vec{B}_p+\vec{B}_Q=-\frac{\mu_0}{2 \pi}+\frac{\mu_0}{\pi}=\frac{\mu_0}{2 \pi} \text { (upward) }

Posted by

SANGALDEEP SINGH

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