Answer :
Answer:
Therefore,
Strength magnetic field at its center, B
[tex]B = 2.51\times 10^{-2}\ T[/tex]
Explanation:
Given:
Turn = N = 500
length of solenoid = l = 0.10 m
Current, I = 4.0 A
Radius, r = 0.01 m
To Find:
Strength magnetic field at its center, B = ?
Solution:
If N is the number of turns in the length, the total current through the rectangle is NI. Therefore, Ampere’s law applied to this path gives
[tex]\int\ {B} \, ds = Bl=\mu_{0}NI[/tex]
Where,
B = Strength of magnetic field
l = Length of solenoid
N = Number of turns
I = Current
[tex]\mu_{0}=Permeability\ in\ free\ space = 4\pi\times 10^{-7}\ Tm/A[/tex]
Therefore,
[tex]B =\dfrac{\mu_{0}NI}{l}[/tex]
Substituting the values we get
[tex]B =\dfrac{4\times 3.14\times 10^{-7}\times 500\times 4}{0.10}=2.51\times 10^{-2}\ T[/tex]
Therefore,
Strength magnetic field at its center, B
[tex]B = 2.51\times 10^{-2}\ T[/tex]