The total length of the wire required is 63 m.
What is current?
The current is the stream of charges which flow inside the conductors when connected across the end of voltage.
Given is a solenoid is configured to produce a magnetic field of 0.027T at its center. it has radius 1.4 cm and length 40cm and the wire can carry a maximum current of 12.0 A.
Radius, r = 1.4cm = 0.014 m
Length l = 40 cm = 0.4 m
If the current is I, then the magnetic field in solenoid is given by
B = μ₀ n I
By substituting the values, we get
0.027 = 4π x 10⁻⁷ x n x 0.4
n = 1792 turns/unit length
Total length of wire = circumference x Turns
L = 2πr x N
where N = nl
Plug the values, we get
L = 2π x 0.014 x1792 x 0.4
L = 63 m
Thus, the total length of the wire is 63 m.
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