A toroid has a core (non-ferromagnetic) of inner radius 25 cm andouter radius 26 cm, around which 3500 turns of a wire are wound.If the current in the wire is 11 A, what is the magnetic field(a) outside the toroid, (b) inside the core of the toroid, and (c) in the empty space surrounded by the toroid.
Given data: The inner radius of the toroid is 25 cm , the outer radius of the toroid is 26 cm , the numbers of turns on the coil are 3500 and the current in the coil is 11 A .
a)
The value of magnetic field outside the core of a toroid is zero.
b)
The length of toroid is given as,
l = 2 π [ r 1 + r 1 2 ]
Where, the inner radius of the toroid is r 1 , the outer radius of the toroid is r 2 and the length of the toroid is l .
By substituting the given values in the above formula, we get
l = 2 π ( 0.25 + 0.26 2 ) = 0.51 π m
The magnetic field inside the core of a toroid is given as,
B = μ ° N I l
Where, the permeability of free space is μ 0 , the numbers of turns are N , the current in the coil is I and the magnetic field inside the core is B .
By substituting the given values in the above formula, we get
B = 4 π × 10 − 7 × 3500 × 11 0.51 π = 3.0 × 10 − 2 T
Thus, the magnetic field inside the toroid is 3.0 × 10 − 2 T .
(c)
The magnetic field in empty space surrounded by the toroid will be zero because the magnetic field will not be varied in empty space surrounded by the toroid.
Given data: The inner radius of the toroid is
a)
The value of magnetic field outside the core of a toroid is zero.
b)
The length of toroid is given as,
Where, the inner radius of the toroid is
By substituting the given values in the above formula, we get
The magnetic field inside the core of a toroid is given as,
Where, the permeability of free space is
By substituting the given values in the above formula, we get
Thus, the magnetic field inside the toroid is
(c)
The magnetic field in empty space surrounded by the toroid will be zero because the magnetic field will not be varied in empty space surrounded by the toroid.
