COMEDK 2023 Shift 1 Paper

The magnetic field at the center of a current-carrying circular coil is given by the formula:
B=‌

µ0I

2R

where,
B is the magnetic field at the center of the coil,
µ0 is the permeability of free space (4π×10−7T⋅m∕A),
I is the current passing through the coil, and
R is the radius of the coil.
Let's determine the magnetic field before and after the radius of the coil is doubled.
Initially, let the magnetic field be B1 with coil radius R. According to the formula:
B1=‌

µ0I

2R

After the radius of the coil is doubled, the new radius is 2R. Let the new magnetic field be B2. Thus,
B2=‌

µ0I

2(2R)

=‌

µ0I

4R

The ratio of the initial magnetic field to the final magnetic field would be:
‌

B1

B2

=‌

‌ µ0I 2R

µ0I 4R

By simplifying the equation, we cancel out µ0,I, and R as they are common in both the numerator and the denominator, leaving:
‌

B1

B2

=‌

2R

R

×‌

4

2

=2
This means the ratio of the magnetic field before the doubling of the radius to after is 2:1. Therefore, the correct answer is:
Option B: 2:1