A current-carrying solenoid has a paramagnetic core. At a temperature of 300 K , the magnetic field inside the solenoid is found to be 0.06 % greater than it would be if the core were empty space. If the temperature of the core is increased to 450 K , the new percentage increase in the magnetic field will be :

Step-by-step solution

The percentage increase in the magnetic field due to the insertion of a core is given by: B ( %) = 100 % where is the magnetic susceptibility of the core material. For a paramagnetic material, Curie's Law states that the magnetic susceptibility is inversely proportional to the absolute temperature T : 1 T Therefore, the percentage increase in the magnetic field is also inversely proportional to the temperature: B₂ ( %) B₁ ( %) = T₁ T₂ Given T₁ = 300 K , B₁ ( %) = 0.06 % , and T₂ = 450 K : B₂ ( %) = 0.06 % 300 450 B