Question

a toroid has a core of inner radius 20 cm and outer radius 22cm around which 4200 turns of a wire are wound if the current in the wire is 10 ampere what is the magnetic field (I) inside the core of toroid (ii) outside the toroid and(iii) in the empty space surrounded by the toroid

Answer 1

Answer:

Explanation:

(i) The magnetic field inside the core of toroid:

=> Suppose, Inside the solenoid,take point 'p' into the open space from the centre (o) at the r1 distance.  

=>now, think about an amperean loop of radius 'r1'.

=> Suppose, 'B1' is the magnetic field at point 'p'.

=> According to the Ampere's circuital theorem,

$\int\limits$ B1 *dl = μ₀* I  

=> Here, the loop doesn't enclose any current.

∴ I =0

Hence, B1= 0.

(ii)  The magnetic field outside the toroid:

=> Think about 'q' point outside the toroid.  

=> suppose it is present at r2 distance from the centre (o).

=> The magnetic field is suppose B2.

∴ $\int\limits$B2* dl = μ₀*I

=> Here, magnetic field due to the current in both the upper as well as lower part of each loop neutralize each other.  

=> Thus,  the magnetic field outside is obtained zero.

∴ B2= 0  

(iii)  The magnetic field in the empty space surrounded by the toroid:  

=> Take the pointt 'R'at the distance of 'r' from the centre (o). It is well inside the toroid.

=> Suppose,  the magnetic field is B here.

=> Thus, According to the ampere's circuital law:

$\int\limits$B * dl = μ₀* N * I  

Where,

N = the total no of turns of the toroid

=> But N=2π*r*n

∴ B*2π*r = μ₀ * 2π * r * n * i

Hence, B = μ₀ * n * i.