The Relationship Between Magnetic Field and Current in a Loop

Ampere's Law and Current Calculation

Ampere's law states that the magnetic field around a closed loop is directly proportional to the current passing through the loop and inversely proportional to the distance from the center of the loop. The formula for Ampere's law is:

B = (μ₀ * I) / (2 * π * r)

Where:

• B is the magnetic field
• I is the current
• μ₀ is the permeability of free space (a constant)
• r is the radius of the loop

Given that the magnetic field B is 2.5 mT and the radius of the loop is 0.5 cm, we can rearrange the formula to solve for the current I:

0.0025 T = (4π * 10^-7 T m/A * I) / (2 * π * 0.5 cm)

Simplifying the equation and converting cm to meters, we get:

0.0025 = (4π * 10^-7 I) / 0.01

Further simplification leads to:

I = (0.0025 * 0.01) / (4π * 10^-7)

Therefore, the current flowing through the loop is approximately 1.96 amperes.