Question

Question 4.15: 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

Class 12 - Physics - Moving Charges And Magnetism Moving Charges And Magnetism Page-170

Answer 1

the magnetic field required is 100G in a length of 10cm =0.1m . so, the solenoid have a length larger than 0.1 m . the maximum current capacity of wire is 15A, so less than 15A should flow in wire.
now using formula,
$B=\frac{\mu_0NI}{l}$

here, B = 100G =100 × 10^-4 T
so, 100 × 10^-4 = 4π × 10^-7 × $\frac{NI}{l}$
or, $\frac{NI}{l}$=7961.8

now, we can think of a possible combination with I = 10A and total length of solenoid l = 50cm = 0.5 m
so, (N × 10)/0.5 = 7961.8
N = 398.09 turns ≈ 400 turns

so, one combination for the desired 100G magnetic field in a length 10cm can be a total length of solenoid of 50cm and current in the solenoid of 10A and total turns nearly 400.

Answer 2

Answer:

the magnetic field required is 100G in a length of 10cm =0.1m . so, the solenoid have a length larger than 0.1 m . the maximum current capacity of wire is 15A, so less than 15A should flow in wire.

now using formula,

here, B = 100G =100 × 10^-4 T

so, 100 × 10^-4 = 4π × 10^-7 ×  

or, =7961.8

now, we can think of a possible combination with I = 10A and total length of solenoid l = 50cm = 0.5 m

so, (N × 10)/0.5 = 7961.8

N = 398.09 turns ≈ 400 turns

so, one combination for the desired 100G magnetic field in a length 10cm can be a total length of solenoid of 50cm and current in the solenoid of 10A and total turns nearly 400.

Explanation: