Question

You have a 1.50-m-long copper wire. You want to make an n-turn current loop that generates a 0.800 mT magnetic field at the center when the current is 1.10 A. How many turns should the loop have?

Answer 1

To determine the number of turns required to create a magnetic field of 0.800 mT at the center of a current loop, we can use the formula for the magnitude of the magnetic field inside a current loop.

Step-by-step explanation:

To determine the number of turns required to create a magnetic field of 0.800 mT at the center of a current loop, we can use the formula for the magnitude of the magnetic field inside a current loop:

B = (μ₀ * I * N)/(2 * π * r)

Where B is the magnetic field, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), I is the current, N is the number of turns, and r is the radius of the loop.

Substituting the given values into the formula, we can solve for N:

N = (B * 2 * π * r)/(μ₀ * I) = (0.800 * 2 * π * 0.750)/(4π × 10⁻⁷ * 1.10) ≈ 1,450 turns