An iron ring of relative permeability u has windings of insulated copper wire of n turns per metre.when the current in the windings is I..find expression for magnetic field of ring
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29
Given,
Relative permeability = u then, permeability of iron = μ₀u
number of turns per meter = n
current through it = I
Now, At center of solenoid { if a current carrying conductor tightly wounded over a wire , system named as solenoid } , cut an element of thickness dx at x meter from its center .
so, number of turns in dx element is N = ndx
Now, use Biot savart law,
B = μ₀uNiR²/(R² + x²)^(3/2) , Let R is the radius of circular part
= μ₀unidxR²/(R² + x²)^(3/2)
= μ₀uniR²dx/(R² + x²)^(3/2)
After integration we get, Magnetic field at center when length of wire is infinite
B = μ₀unI
Hence, answer is B = B = μ₀unI
Relative permeability = u then, permeability of iron = μ₀u
number of turns per meter = n
current through it = I
Now, At center of solenoid { if a current carrying conductor tightly wounded over a wire , system named as solenoid } , cut an element of thickness dx at x meter from its center .
so, number of turns in dx element is N = ndx
Now, use Biot savart law,
B = μ₀uNiR²/(R² + x²)^(3/2) , Let R is the radius of circular part
= μ₀unidxR²/(R² + x²)^(3/2)
= μ₀uniR²dx/(R² + x²)^(3/2)
After integration we get, Magnetic field at center when length of wire is infinite
B = μ₀unI
Hence, answer is B = B = μ₀unI
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Ananthukerala:
If i solve it like considering it a solenoid is it correct ?? Answer will be same..
Off course we should use solenoid concept here , becoz iron ring wounded in copper wire in such a way that number of terms per meter is n . Means ring have length too. e.g., solenoid .
what if i used the toroid formula to get the magnetic field expression?
Ohh you can't use toroi here , as you know when solenoid wound like a ring then system named as toroid.
What if i have used the application of biot savart law to derive the expression
Magnetic field due to a circular loop
but here used number of tuns per meter , it shows solenoid . then how you can use circular loops
Answered by
8
Answer:Given,
Relative permeability = u then, permeability of iron = μ₀u
number of turns per meter = n
current through it = I
Now, At center of solenoid { if a current carrying conductor tightly wounded over a wire , system named as solenoid } , cut an element of thickness dx at x meter from its center .
so, number of turns in dx element is N = ndx
Now, use Biot savart law,
B = μ₀uNiR²/(R² + x²)^(3/2) , Let R is the radius of circular part
= μ₀unidxR²/(R² + x²)^(3/2)
= μ₀uniR²dx/(R² + x²)^(3/2)
After integration we get, Magnetic field at center when length of wire is infinite
B = μ₀unI
Hence, answer is B = B = μ₀unI
Explanation:
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