When a certain material is inserted into the empty space of a current-carrying solenoid, the magnetic field inside the solenoid increases by 0.0025 % . The relative permeability of the inserted material is :

Step-by-step solution

The percentage increase in the magnetic field is given by: B ( %) = B_ new - B_ old B_ old 100 % Since B_ old = ₀ n i and B_ new = n i = _r ₀ n i , we have: B ( %) = _r ₀ n i - ₀ n i ₀ n i 100 % = ( _r - 1) 100 % We know that _r - 1 = , where is the magnetic susceptibility. Given that the percentage increase is 0.0025 % : 100 = 0.0025 = 0.0025 100 = 2.5 10⁻⁵ The relative permeability _r is: _r = 1 + = 1 + 0.000025 = 1.000025 Answer: 1.000025