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.

\[\Rightarrow  B_{net}    =    B_1  +  B_2 \] 

\[                             =   \left( \frac{2 \times {10}^{- 7} \times 5}{1} + \frac{2 \times {10}^{- 7} \times 5}{1} \right)\] 

  = 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.

\[\Rightarrow  B_{net}    =    B_1  +  B_2 \] 

\[                             =   \left( \frac{2 \times {10}^{- 7} \times 5}{1} + \frac{2 \times {10}^{- 7} \times 5}{1} \right)\] 

               = 2 × 10⁻⁶ T    (Along the negative z-axis)