Question

Q5. A solenoid of length 100 cm is wound uniformly with 10 000 turns

of wire. It carries a current of 4 A. What is the value of following?
i. Magnetic field on the axis of the solenoid at the center.
ii. Magnetic field on the axis at the end.
​

Answer 1

i) 0.05 T

ii) 0.025 T

Step-by-step explanation:

current I = 4 A

length of solenoid L = 100 cm = 1 m

number of turns N = 10000 turns

number of turns per unit length n = N/L = 10000/1 = 10000 turns/meter

i) magnetic field on the axis of the solenoid at the center

B = μ
`nI`

where μ is vacuum permeability = 4π×10−7 H/m = 1.256 x
`10^(-6)` H/m

B = 1.256 x
`10^(-6)` x 10000 x 4 = 0.05 T

ii) magnetic field on the axis at the end will be equal to

B = (μ
`nI`) ÷ 2

this is based on the assumption that the length of the solenoid is far greater than than the diameter of the solenoid. Therefore,

B = 0.05 ÷ 2 = 0.025 T