The core of a toroid having 3000 turns has inner and outer radii of 16 cm and 17 cm respectively . The magnetic field in the core for a current of `0.07` A is 2.5 T . What is relative permeability of the core ?

Explanation

`B = mu_(0) mu_(r) ` ni
`= mu_(0) mu_(r) (N)/(2pi r) xx i`
`= (mu_(0))/(4pi) mu_(r) xx (2 "Ni")/(r)`
`2.5 = 10^(-7) xx mu_(r) xx (2xx 3000 xx 0.07)/((33)/(2) xx 10^(-2))`
`2.5 = (10^(-7) xx 4 xx 3 xx 7 xx 10^(-3) xx mu_(r))/(33)`
`27.5 = 28 xx 10^(-4) xx mu_(r)`
`mu_(r) = (27.5)/(28) xx 10^(4)`
`= 0.9821429 xx 10^(4)`
`mu_(r) = 9821`