Question

Two concentric circular loops, one of radius $R$ and the other of radius $2 R$, lie in the $x y$-plane with the origin as their common centre, as shown in the figure . The smaller loop carries current $I_{1}$ in the anti-clockwise direction and the larger loop carries current $I_{2}$ in the clock wise direction, with $I_{2}>2 I_{1}, \vec{B}(x, y)$ denotes the magnetic field at a point $(x, y)$ in the $x y$-plane. Which of the following statement (s) is ( are ) correct?

• A. $\vec{ B }( x , y )$ is perpendicular to the $xy$-plane at any point in the plane
• B. $|\vec{ B }( x , y )|$ depends on $x$ and $y$ only through the radial distance $r =\sqrt{ x ^{2}+ y ^{2}}$
• C. $|\vec{ B }( x , y )|$ is non-zero at all points for $r < R$
• D. $\vec{ B }( x , y )$ points normally outward from the $xy$-plane for all the points between the two loops

Answer 1

Answer: (B)

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

Answer 2

B

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