Calculate the lifting force
The equation for the lifting force of an electromagnet is
#color(blue)(bar(ul(|color(white)(a/a) F = ((nI)^2µ_0A)/(2g^2)color(white)(a/a)|)))" "#
where
#n = # the number of terms
#I = # the current
#µ_0 = # the permeability of air
#A = # the area of the poles
#g =#the gap between the object and the electromagnet
In this problem, you are changing only the current, so you can write
#F_2/F_1 = ((color(red)(cancel(color(black)(n)))I_2)^2color(red)(cancel(color(black)(µ_0A))))/((color(red)(cancel(color(black)(n)))I_1)^2color(red)(cancel(color(black)(µ_0A)))) × stackrelcolor(blue)(1)(cancel(color(black)2g^2))/(color(red)(cancel(color(black)(2g^2))))#
#F_2/F_1 = (I_2/I_1)^2#
#F_2 = F_1 × (I_2/I_1)^2#
In this problem.
#F_1 = "12.0 N"; I_1 = "5.0 A"#
#F_2 = ?;color(white)(mml) I_2 = "8.0 A"#
∴ #F_2 = "12.0 N" × ((8.0 color(red)(cancel(color(black)("A"))))/(5.0 color(red)(cancel(color(black)("A")))))^2 = 30.7 N#
Calculate the mass that can be lifted
#F = mg#
#M = F/g = (30.7 color(red)(cancel(color(black)("N"))))/(9.81 color(red)(cancel(color(black)("m·s"^"-2")))) × ("1 kg"·color(red)(cancel(color(black)("m·s"^"-2"))))/(1 color(red)(cancel(color(black)("N")))) = "3.1 kg"#
The electromagnet can lift a mass of 3.1 kg.
