COMEDK 2024 Shift 1 Paper

To determine the ratio of the magnetic field induction at the origin due to the smaller coil to that of the bigger one, we need to use the formula for the magnetic field along the axis of a circular coil carrying current. This is given by:
B=‌

µ0Ia2

2(x2+a2)3∕2

where:
B is the magnetic field at a distance x from the coil along its axis.
µ0 is the permeability of free space.
I is the current in the coil.
a is the radius of the coil.
x is the distance from the coil to the point where the field is being calculated.
For the smaller coil (radius a and distance x ):
B1=‌

µ0Ia2

2(x2+a2)3∕2

For the larger coil (radius 2a and distance 2x ):
The ratio of the magnetic field induction at the origin due to the smaller coil to that of the larger coil can now be calculated as follows:
Therefore, the ratio of the magnetic field induction at the origin due to the smaller coil to that of the bigger one is:
Option A: 2:1