The magnetic field at the center of a current-carrying circular coil is given by the formula:
B=‌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=‌After the radius of the coil is doubled, the new radius is
2R. Let the new magnetic field be
B2. Thus,
B2=‌=‌ The ratio of the initial magnetic field to the final magnetic field would be:
‌=‌By simplifying the equation, we cancel out
µ0,I, and
R as they are common in both the numerator and the denominator, leaving:
‌=‌×‌=2This 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