A10.3 g wire has a density of 10.7 g/cm3 and a resistivity of 6.9 × 10−8 ω · m. the wire has a resistance of 59 ω. how long is the wire?

28.65 m

First we need to find the cross sectional area of the wire and for that we need to find the radius of the wire, r

density = mass/ volume

10.7 = 10.3 / volume

volume = 10.3/10.7

            = 0.96cm³

1,000,000 cubic centimeters = 1 cubic meter

so

             0.96/1,000,000 = 9.6 x 10^-7m

formula for volume

9.6 x 10^-7 = πr²(L)

r = √(9.6 x 10^-7/π(L))

Formula for resistivity

59 = 6.9 × 10^−8(L) /  πr²

59 = 6.9 × 10^−8(L) /  π(9.6 x 10^-7/π(L)

59 = 6.9 × 10^−8(L) /  9.6 x 10^-7/(L)

59 /6.9 × 10^−8 = L / 9.6 x 10^-7/(L)

L² = 59 (9.6 x 10^-7) / 6.9 × 10^−8

L² = 820.87

L = √ 820.87

= 28.65m

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.