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

\[B_w = \frac{\mu_0 i}{2\pi d} = \frac{4\pi \times {10}^{- 7} \times 1}{2\pi \times 0 . 02}\] 
\[ \Rightarrow B_w = 1 \times {10}^{- 5} T\]

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