A uniform magnetic field of 100 G `(IG=10^(-4)T)` exists in a region of length about 10 cm and area of cross- section about `10^(-3)m^(2)`. The maximum current carrying capacity of a given coil of wire is 15A and the number of turns per unit length that can be wound round a core is at most 1000 turns `m^(-1)`. How would you utils the coil to design a solenoid for the required purpose ? Assume the core is not ferromagnetic.

Explanation

For maximum number of turns the current through the solenoid is given by,
`I=(Bl)/(mu_(0)N)=(B)/(mu_(0)((N)/(l)))[ :. B=Mu_(0)=*(N)/(l)*I]`
`=(100xx10^(-4))/(4pi xx10^(7)xx100)A=7.96A~~8A`
The length of the solenoid should be much more than its diamter.
For a current of 15A to flow through the solenoid, number of turns per unit length has to be decreases [as`I prop (I)/(N) prop (1)/(N//l]`
`:. (I')/(I)=(N//l)/(N'//l') or, (15)/(8) =(1000)/(N'//l)`
`:. (N')/(l')=(100xx8)/(15)=533~~550 "turns" *m^(-1)`.