The percentage increase in magnetic field B when the space within a current carrying solenoid is filled with a medium of susceptibility 0.004 is

Step-by-step solution

The magnetic field inside a current-carrying solenoid in vacuum is given by B₀ = ₀ n I . When the space is filled with a medium of magnetic susceptibility _m , the magnetic field becomes B = _r B₀ , where _r is the relative permeability of the medium. The relative permeability is related to susceptibility by _r = 1 + _m . Given _m = 0.004 , we have _r = 1 + 0.004 = 1.004 . The new magnetic field is B = 1.004 B₀ . The increase in magnetic field is B = B - B₀ = 1.004 B₀ - B₀ = 0.004 B₀ . The percentage increase is B