Two infinitely long wires carry currents $4 \mathrm{~A}$ and 3A placed along $X$-axis and $Y$-axis respectively. Magnetic field at a point $P(0,0$, d) $m$ will be ...... $\mathrm{T}$.

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Aicharya · Accepted Answer

Magnetic field at point $P$ due to $I_x$ $ \begin{aligned} \mathbf{B}_x & =\frac{\mu_0 I_x}{2 \pi d}(-Y \text {-direction }) \\ \text { or } \quad \mathbf{B}_x & =-\frac{\mu_0 \cdot 4}{2 \pi d} \hat{\mathbf{j}} \end{aligned} $ Similarly, magnetic field at point $P$ due to $I_y$,

$ \Rightarrow \quad \mathbf{B}_y=\frac{\mu_0 \cdot 3}{2 \pi d} a \hat{\mathbf{i}} $ $\therefore$ Resultant magnetic field, $ \begin{aligned} B & =\sqrt{B_x^2+B_y^2} \\ & =\frac{\mu_0}{2 \pi d} \sqrt{4^2+3^2} \\ B & =\frac{5 \mu_0}{2 \pi d}\left(\text { at }-45^{\circ} \text { from } X \text {-axis }\right) \end{aligned} $

Two infinitely long wires carry currents $4 \mathrm{~A}$ and 3A placed along $X$-axis and $Y$-axis…

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