Login/Sign Up
A magnetic field of 100 G is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about ${{10}^{-3}}$ m2. 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 around 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.
A magnetic field of 100 G is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about ${{10}^{-3}}$ m2. 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 around 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.
CBSE | Class 12 | Moving Charges and Magnetism | NCERT | Physics
A magnetic field of 100 G is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about ${{10}^{-3}}$ m2. 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 around 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.

Magnetic field strength, B is given as $100 \times {10^{-4}}T$

Number of turns per unit length, N is given as 1000 turns/m

Current carrying capacity of the coil is given as 15 A

Permeability of free space, μ0 is given as $4\pi  \times {10^{-7}}Tm{A^{-1}}$

Magnetic field is given by:

B = μ0 NI/l

⇒ NI/l = B/μ0 

$ = (100 \times {10^{-4}})/(4\pi  \times {10^{-7}})$

NI/l = 7961

We can now explore a possible combination. Let I = 10 A and l = 0.5 m be the current and length of the solenoid, respectively.

So we get

(N x 10)/0.5 =  7961

N = 398 turns ≈ 400 turns

The length is around 50 cm, the number of spins is about 400, and the current is about 10 A. These specifics are not unusual. Limits can be adjusted to some extent.

i

More Material