Question

Two insulated wires of infinite length are lying mutually at right angles to each other as shown in the figure. Current of 2 A and 1.5 A respectively are flowing in them. The value of magnetic induction at point P will be :

• A. $2\times {10}^{-3}N/A-m$
• B. $2\times {10}^{-5}N/A-m$
• C. zero
• D. $2\times {10}^{-4}N/A-m$

Answer 1

The correct option is B $2\times {10}^{-5}N/A-m$

Magnetic field due to a infinite line current at distance $x\Rightarrow \frac{{\mu }_{0}I}{2\pi x}$
$\Rightarrow$Magnetic field at point P$\Rightarrow$ magnetic field due to wire 1 + magnetic field due to wire 2
$\Rightarrow \frac{{\mu }_0\left(2\right)}{2\pi \left(0.04\right)}+\frac{{\mu }_0\left(1.5\right)}{2\pi \left(0.03\right)}$
$\Rightarrow {10}^{-5}+{10}^{-5}=2\times {10}^{-5}\frac{N}{A-m}$