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To find the inductance of a coil, we can use the formula for the inductance of a solenoid, which is given by:

[L = mu N^2 A / l]

where:

– (L) is the inductance,

– (mu) is the permeability of the core material,

– (N) is the number of turns,

– (A) is the cross-sectional area,

– (l) is the length of the coil.

Given in the question:

– (mu = 3.5) (Assuming the unit here is Henrys per meter (H/m) since it’s about permeability and no specific unit is given),

– (N = 100) turns,

– The length ((l)) of the coil is (2m),

– The area ((A)) is thrice the length. However, to calculate area from length doesn’t directly compute without additional context, as length and area are not directly convertible. Assuming it means the side length of a square cross-section is thrice some basic unit, or perhaps a misunderstanding in the question’s phrasing. If it meant the area is proportional to the length in some manner not clearly defined, clarification is needed. Assuming a more typical approach where we define an area based off given or assumed dimensions: if by “thrice the length”, it means for example, the dimension contributing to the area is 3 times some value

a

Explanation: The inductance is given by L = μ N2A/l, where μ= μoμr is the permeability of

air and the material respectively. N = 100 and Area = 3 X 2 = 6. L = 4π X 10-7 X 1002 X

6/2 = 131.94mH.