Two long thin, parallel conductors carrying equal currents in the… - Vidyadip

MCQ

Two long thin, parallel conductors carrying equal currents in the same direction are fixed parallel to the $x$-axis, one passing through $y = a$ and the other through $y = -a$. The resultant magnetic field due to the two conductors at any point is $B$. Which of the following are correct?

A
$B = 0$ for all points on the $x$-axis
B
At all points on the $y-$axis, excluding the origin, $B$ has only $a\,\, z-$ component.
C
At all points on the $z-$axis, excluding the origin, $B$ has only $a\,\, y-$ component.
✓
All of the above

✓

Answer

Correct option: D.

All of the above

d
$(A)$ $\mathrm{B}=\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{a}}-\frac{\mu_{0} \mathrm{I}}{2 \pi \mathrm{a}}=0$

$(B)$ On $y-axis$ say at $(y, 0,0)$

$B=\frac{-\mu_{0} I}{2 \pi(a+y)} \hat{k}+\frac{\mu_{0} I}{2 \pi(a-y)} \hat{k}$

So except at origin, $B$ has only $z-components$

$B$ cannot has $x-component$ as $B$ is perpendicular to direction of $I .$

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