A researcher would like to perform an experiment in a zero magnetic field, which means that the field of the earth must be canceled. Suppose the experiment is done inside a solenoid of diameter 1.0 m, length 3.0 m, with a total of 5000 turns of wire. The solenoid is oriented to produce a field that opposes and exactly cancels the 52 μT local value of the earth's field. What current is needed in the solenoid's wires?

I = 2.48 10⁻² A

Explanation:

The magnetic field produced by a solenoid disproportionate to the density of turns and the current passing through the wire

B = μ₀ n I

Where μ₀ is the magnetic permeability that you are worth 4π 10⁻⁷ N/A²

Let's calculate the density of turns.

n = N / L

n = 5000 / 3.0

n = 1666.67

Let's reduce the field to SI units

B = 52 μT = 52 10⁻⁶ T

Let's calculate the current

I = B / μ₀ n

I = 52 10⁻⁶ / (4π 10⁻⁷ 1666.67)

I = 2.48 10⁻² A