First slide

Magnetic field due to a straight current carrying wire

Question

Two long parallel wires P and Q are held perpendicular to the plane of paper with distance of 5 m between them. If P and Q carry current 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

Easy

A

$μ_{0} / 17$
B

$\sqrt{3} μ_{0} / 2 π$
C

$μ_{0} / 2 π$
D

$3 μ_{0} / 2 π$

Solution

$\begin{array}{l} B = \frac{μ_{0}}{4 π} \times \frac{2 i_{2}}{(r / 2)} - \frac{μ_{0}}{4 π} \times \frac{2 i_{1}}{(r / 2)} \\ = \frac{μ_{0}}{4 π} \times \frac{4 (i_{2} - i_{1})}{r} = \frac{μ_{0}}{π} \times \frac{(5 - 2 \cdot 5)}{5} = \frac{μ_{0}}{2 π} \end{array}$

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