Question

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 4.6 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?
Express your answer to two significant figures and include the appropriate units.

Answer 1

I = 3.81 x 10⁴ A

Step-by-step explanation:

The magnetic field of a solenoid must be equal to the field of earth:

`Field\ of\ Earth = Field\ of\ Solenoid\\52\ T = \mu n I\\I = (52)/(\mu n)`

where,

I = current passing through solenoid = ?

μ = permeability of free space = 4π x 10⁻⁷ N/A²

n = no. of turns per unit length =
`(5000\ turns)/(4.6\ m)` = 1086.96 /m

Therefore,

`I = (52\ T)/((4\pi\ x\ 10^(-7)\ N/A^2)(1086.96\ /m))`

I = 3.81 x 10⁴ A