A magnetic field of 100 G `(1 G = 10^(-4) T) `is required which is uniform in a region of linear dimension 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 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns `m^(-1)`. Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

Explanation

Magnetic field inside the current carrying long solenoid is,
`B=mu_(0)nI`
`thereforenI=B/mu_(0)`
`thereforenI=(100xx10^(-4))/(4pixx10^(-7))`
`thereforenI=(100000)/(4xx3.14)`
`thereforenI=7962A/m`
If we keep `n=1000("turn")/m` = max then we have to pass current through a solenoid I = 7.962 A. Here, we should choose length of solenoid quite big as compared to radius of its cross-section, so as to have almost uniform magnetic field in the middle region of solenoid as per the statement.