Answer :
Correct option is B) The radius of a current-carrying circular loop can be determined from the magnetic field at its center using the formula that involves the magnetic constant, current, and magnetic field strength. After substituting the provided values into the formula and solving, the radius of the loop is found to be 1.57 * 10^{-4} m.
The question pertains to the magnetic field at the center of a current-carrying circular loop and how it relates to the radius of the loop. The magnetic field (B) at the center of a circular loop of wire carrying a current (I) is given by the formula B = (rac{ ext{ extmu}_0}{2}) * (rac{I}{R}) for a loop in the air, where ext{ extmu}_0 is the magnetic constant (also known as the permeability of free space), R is the radius of the loop, and I is the current. Using the values provided for B and I in the question, we can rearrange this formula to solve for R:
B = (rac{ ext{ extmu}_0}{2}) * (rac{I}{R})
2 mt = (rac{4 ext{ extpi} * 10^{-7} ext{H/m}}{2}) * (rac{500 * 10^{-3} A}{R})
R = (rac{4 ext{ extpi} * 10^{-7} ext{H/m}}{2}) * (rac{500 * 10^{-3} A}{2 * 10^{-3} T})
After solving for R, we find that the correct answer is (b) 1.57 * 10^{-4} m.
