Derivation fir TOROID (ENDLESS LOOP)
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A toroid is a hollow circular ring on which a large number of turns of an insulated copper wire are closely wounded. for toroid of solenoid carring current the magnetic field at any point.
(1) outside the toroid
(2) inside the open space in the toroid is zero.
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If the solenoid had been of infinite length, there will be no ends and hence everywhere inside the solenoid the field will be uniform , equal to " μ₀ni "while outside it be zero .
This actually happens in a toroid which is a solenoid bent in a circular shape so, that it two ends join each other.
Hence,
Magnetic field inside a toroidal solenoid of radius R and having N number of turns and carring current I
B = μ₀ni = μ₀Ni/2πR
where, n = N/2πR = no of turns per unit length.
when two different radius e.g a and b
then R = (a + b)/2
(1) outside the toroid
(2) inside the open space in the toroid is zero.
__________________________________________________________________
If the solenoid had been of infinite length, there will be no ends and hence everywhere inside the solenoid the field will be uniform , equal to " μ₀ni "while outside it be zero .
This actually happens in a toroid which is a solenoid bent in a circular shape so, that it two ends join each other.
Hence,
Magnetic field inside a toroidal solenoid of radius R and having N number of turns and carring current I
B = μ₀ni = μ₀Ni/2πR
where, n = N/2πR = no of turns per unit length.
when two different radius e.g a and b
then R = (a + b)/2
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