The region inside a current carrying torodial winding is filled with tungsten of susceptibility `6.8 xx 10^(-5)`. What is the percentage increase in the magnetic field in the presence of the material with respect to the magnetic field without it ?

Explanation

The magnetic field in the current carrying torodial winding without tungsten is
`B= muH`
`therefore (B- B_0)/( B_0) = (mu-mu_(0 ) )/( mu_(0) ) " "…(1)`
But `mu= mu_(0) (1+ chi_(m) ) `
`therefore (mu)/( mu_0) = 1+ chi_(m) `
`therefore (mu)/( mu_0) -1 = chi_(m)`
`therefore (mu- mu_0)/( mu_0) = chi_m`
`therefore` Using this equation,
`(B- B_0)/( B_0) = chi_m`
`therefore` Percentage increase in the magnetic field in presence of tungsten is
`(B- B_0)/( B_0) xx 100 = (6.8 xx 10^(-5) )xx 100`
`= 6.8 xx 10^(-3)`%