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 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 > 2I 1 . 
(x, y) denotes the magnetic field at a point (x, y) in the xy-plane. Which of the following statement(s) is(are) correct?
(x, y) is perpendicular to the xy-plane at any point in the plane
(x, y) | depends on x and y only through the radial distance 
(x, y) | is non-zero at all points for r < R
(x, y) points normally outward from the xy-plane for all the points between the two loops
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(a, b)
Consider a circular loop of radius r in x-y plane and having centre at origin
for given r
Here 
is in xy plane 
B is normal to plane (B can't be in xy plane as its magnetic lines would have been in radial direction)
Also, for given r, B must be same in magnitude for all points on loop of radius r.
At centre 
(inwards)
For point P, Let field of inner loop increases xi times and that of outer loop increases x 2 times
magnetic field at P
For 
B changes more rapidly as point P come closer to circumference.
Or i 2 > 2i 1 (which is given condition)
So, there are points inside inner loop where magnetic field will be zero.
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