Magnetic Filed Due to Torroid
Description:
A toroid is circular shape material that is wrapped up by current conducting wire.
There is a toroid with turn density ‘n’, and current i flowing through it.
1. B at a point outside the toroid at a distance r.
Consider an Amperean loop passing through P.
By applying Amperean Law -
∮ B.→dl→ = μ0i
We can observe net current is zero
∴ B.dl = 0
B = 0
Hence, Magnetic field outside toroid is zero.
2. B at a point inside the toroid.
Consider an Amperean loop passing through P.
By applying Amperean Law -
∮ B.→dl→ = μ0i
Current through loop is again zero
∴ B = 0
3. B at a point within the toroid.
Consider an Amperean loop passing through P which has center same as that of toroid.
The magnetic field B is along the Amperean loop and it is constant.
θ is also zero.
∮ B.dl = B ∮ dl cosθ = B2πr
Current threading through the loop-
iTotal = nl×i
iTotal = n2πr×i
Apply Ampere’s law
Putting values B2πr = μ0n2πri
B = μ0ni