Question

Two long, straight wires, each carrying a current of 5 A, are placed along the x- and y-axis respectively. The currents point along the positive directions of the axes. Find the magnetic fields at the points (a) (1 m, 1 m), (b) (−1 m, 1 m), (c) (−1 m, −1 m) and (d) (1 m, −1 m).

Answer 1

Given:
Magnitude of current, I = 5 A
Separation of the point from the wire, d = 1 m
Thus, the magnitude of magnetic field due to current in the wires is given by
$B_1=B_2=\frac{{\mu }_{0}I}{2\pi d}$


(a) At point (1 m, 1 m), the magnetic fields due to the wires are the same in magnitude, but they are opposite in direction.
Hence, the net magnetic field is zero.

(b) At point (−1 m, 1 m), the magnetic fields due to the wires are in upward direction.
$$\begin{gathered} \Rightarrow B_{\mathrm{net}}=B_1+B_2 \\ =\left(\frac{2\times {10}^{-7}\times 5}{1}+\frac{2\times {10}^{-7}\times 5}{1}\right) \end{gathered}$$
= 2 × 10⁻⁶ T (Along the z-axis)

(c) At point (−1 m, −1 m), the magnetic fields due to the wires are the same in magnitude, but they are opposite in direction.
Hence, the net magnetic field is zero.

(d) At point (1 m, −1 m), the magnetic fields due to the wires are in upward direction.
$$\begin{gathered} \Rightarrow B_{\mathrm{net}}=B_1+B_2 \\ =\left(\frac{2\times {10}^{-7}\times 5}{1}+\frac{2\times {10}^{-7}\times 5}{1}\right) \end{gathered}$$
= 2 × 10⁻⁶ T (Along the negative z-axis)