A long solenoid initially has a vacuum core. When a certain magnetic material is inserted into the core, the magnetic field inside the solenoid increases by 0.15 % . The relative permeability of the core material is:

Step-by-step solution

Let the initial magnetic field inside the solenoid with a vacuum core be B₀ = ₀ n I . When the magnetic material is inserted, the magnetic field becomes B = ₀ _r n I = ₀ (1 + ) n I . The fractional increase in the magnetic field is B B₀ = B - B₀ B₀ = . Given that the percentage increase is 0.15 % , the fractional increase is = 0.15 100 = 0.0015 . The relative permeability of the material is _r = 1 + = 1 + 0.0015 = 1.0015 . Answer: 1.0015