Question

A long, straight wire carrying a current of 1.0 A is placed horizontally in a uniform magnetic field B = 1.0 × 10⁻⁵ T pointing vertically upward figure. Find the magnitude of the resultant magnetic field at the points P and Q, both situated at a distance of 2.0 cm from the wire in the same horizontal plane.

Answer 1

Given:
Uniform magnetic field, B₀ = 1.0 × 10⁻⁵ T (Vertically upwards)
Separation of the point from the wire, d = 2 cm = 0.02 m
The magnetic field due to the wire is given by
$$\begin{gathered} B_{\mathrm{w}}=\frac{{\mu }_{0}i}{2\mathrm{\pi }d}=\frac{4\mathrm{\pi }\times {10}^{-7}\times 1}{2\pi \times 0.02} \\ \Rightarrow B_{\mathrm{w}}=1\times {10}^{-5}\mathrm{T} \end{gathered}$$


Now,
Net magnetic field at point P:
B_P = B_w + B₀ = 2 × 10⁻⁵ T
Net magnetic field at point Q:
B_Q = B_w − B₀ = 0