Single Choice

In a coaxial, straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

Aoutside the cable
Correct Answer
Binside the inner conductor
Cinside the outer conductor
Din between the two conductors

Solution

$$\vec{B} = \vec{B_{outer}} + \vec{B_{inner}}$$
Since the current carried by the outer and and inner are equal and in opposite direction,
magnetic field produced by the cylinders at a point P( distance r from central axis ) is
$$\vec{B_{outer}}= \dfrac{\mu_0}{4\pi}i\dfrac{\vec{dl}\times \vec{r}}{r^3}$$
$$\vec{B_{inner}}= -\dfrac{\mu_0}{4\pi}i\dfrac{\vec{dl}\times \vec{r}}{r^3}$$
$$ \therefore \vec{B} = \vec{B_{outer}} + \vec{B_{inner}} = 0$$

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