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  • Two long parallel wires P and Q are both perpendicular to the plane of the paper with distance of 5 m between them. If P and Q carry currents of 2.5 amp and 5 amp respectively in the same direction

Two long parallel wires P and Q are both perpendicular to the plane of the paper with distance of 5 m between them. If P and Q carry 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{\sqrt{3} \mu_0}{2 \pi}


Option: 4

\frac{\mu_0}{2 \pi}


Answers (1)

When the current flows in both wires in the same direction then magnetic field at half way due to the wire P
\overrightarrow{\mathrm{B}}_{\mathrm{p}}=\frac{\mu_0 \mathrm{I}_1}{2 \pi \frac{5}{2}}=\frac{\mu_0 \mathrm{I}_1}{\pi \cdot 5}=\frac{\mu_0}{2 \pi}\left(\text { where } I_1=2.5 \mathrm{amp}\right)

The direction of \overrightarrow{\mathrm{B}}_{\mathrm{p}} is downward

Magnetic field at half way due to wire Q
\overrightarrow{\mathrm{B}}_{\mathrm{Q}}=\frac{\mu_0 \mathrm{I}_2}{2 \pi_{\frac{5}{2}}^2}=\frac{\mu_0}{\pi} \text { [upward] }
[where\mathrm{I}_2=2.5 \mathrm{amp}. ]
Net magnetic field at half way

\overrightarrow{\mathrm{B}}=\overrightarrow{\mathrm{B}}_{\mathrm{P}}+\overrightarrow{\mathrm{B}}_{\mathrm{Q}} \\
=-\frac{\mu_0}{2 \pi}+\frac{\mu_0}{\pi}=\frac{\mu_0}{2 \pi} \text { (upward) }

Hence, net magnetic field at midpoint  =\frac{\mu_0}{2 \pi}.

Posted by

Sumit Saini

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