Question

A long straight wire carries the current along positive x-direction. Consider four points in space $A(0,1,0),B(0,1,1),C(1,0,1)$ and $D(1,1,1)$. Which of the pairs will have same magnitude of magnetic field?

• A. A and B
• B. A and C
• C. B and C
• D. B and D

Answer 1

Answer: (B), (D)

The correct options are
B A and C
D B and D


We know that magnetic field due to a current carrying infinite length wire is
$B=\frac{{\mu }_{0}I}{2\pi d}$
So for all the points only variable is perpendicular distance $d$.
Since wire lies on $x$ axis,
$\therefore d=\sqrt{y^2+z^2}$
$d_A=1$
$d_B=\sqrt{2}$
$d_B=1$
$d_D=\sqrt{2}$

$\therefore B_A=B_C;B_B=B_D$