Question

Two infinitely long insulated wires are kept perpendicular to each other. They carry currents $I_1=2A$ and $I_2=1.5A$.
i) Find the magnitude and direction of the magnetic field at P.
ii) If the direction of current is reversed in one of the wires. What would be the magnitude of the field B?

• A. $2\times {10}^{-5}T$, normally into the plane of the paper, $2\sqrt{2}\times {10}^{-5}T$
• B. $2\times {10}^{-5}T$,normally out of the plane of the paper, $2\sqrt{2}\times {10}^{-5}T$
• C. $2\times {10}^{-5}T$, normally into the plane of the paper, Zero
• D. $2\times {10}^{-5}T$, normally into the plane of the paper, Zero

Answer 1

The correct option is C $2\times {10}^{-5}T$, normally into the plane of the paper, Zero

$B_1=\frac{{\mu }_0{i}_1}{2\pi r_1}=\frac{2\times {10}^{-7}\times 2}{4\times {10}^{-2}}={10}^{-5}{B}_2=\frac{{\mu }_0{i}_2}{2\pi r_2}=\frac{2\times {10}^{-7}\times 1.5}{3\times {10}^{-2}}={10}^{-5}B=B_1+B_2={10}^{-5}+{10}^{-5}$
$=2\times {10}^{-5}$, normally in to the place of the paper, zero