Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I1 in the anti-clockwise direction and the larger loop carries current I2 in the clockwise direction, with I2 > 2I1. (x, y) denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) current?

Engineering

Physics

Magnetic Field

Amperes Circuital Law and its Applications

Question

Two concentric circular loops, one of radius R and the other of radius 2R, lie in the xy-plane with the origin as their common center, as shown in the figure. The smaller loop carries current I₁ in the anti-clockwise direction and the larger loop carries current I₂ in the clockwise direction, with I₂ > 2I₁. $\vec{B}$ (x, y) denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) current?

$| \vec{B} (x, y) |$ is non-zero at all points for r < R

$| \vec{B} (x, y) |$ depends on x and y only through the radial distance $r = \sqrt{x^{2} + y^{2}}$

$\vec{B} (x, y)$ points normally outward from the xy-plane for all the points between the two loops

$\vec{B} (x, y)$ is perpendicular to the xy-plane at any point in the plane

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(A) $d \vec{B} = \frac{μ_{0} i \vec{dℓ} \times \vec{r}}{4 {πr}^{3}}$

$\vec{dℓ}$ is in xy plane & $\vec{r}$ is also in xy plane

so $d \vec{B}$ is perpendicular to xy plane

(B) Due to symmetry it depends only on $r = \sqrt{x^{2} + y^{2}}$

but as we approach towards first loop B₁ increases to infinity hence B₁ dominates.

So it would be zero at some point between inner loops and centre.