A long wire is bent into shape ABCDE as shown in fig., with
BCD being a semicircle with centre O and radius r metre. A
current of I amp. flows through it in the direction
A → B → C → D → E. Then the magnetic induction at the
point O of the figure in vacuum is
(a) μ₀ [I/2πr + 1/4r]
(b) μ₀ [I/2πr - 1/4r]
(c) μ₀ I / 4r
(d) μ₀ I / πr
Answers
Given that,
A long wire is bent into shape ABCDE. BCD being a semicircle with centre O.
Radius = r
Current = I
Magnetic field at O due to the semi-infinite segment AB is half of that due to an infinite wire
The magnetic induction is
Magnetic field at O due to the semi-infinite segment DE is half of that due to an infinite wire
The magnetic induction is
Magnetic field at O due to the semi-infinite segment BCD is half of that due to an infinite wire
The magnetic induction is
The magnetic field due to semi circular portion is half of that due to a circular wire.
We need to calculate the magnetic induction at the point O
Using formula for magnetic induction
Put the value into formula
Hence, The magnetic induction at the point O is
(a) is correct option.
Answer:
Given that,
A long wire is bent into shape ABCDE. BCD being a semicircle with centre O.
Radius = r
Current = I
Magnetic field at O due to the semi-infinite segment AB is half of that due to an infinite wire
The magnetic induction is
Magnetic field at O due to the semi-infinite segment DE is half of that due to an infinite wire
The magnetic induction is
Magnetic field at O due to the semi-infinite segment BCD is half of that due to an infinite wire
The magnetic induction is
The magnetic field due to semi circular portion is half of that due to a circular wire.
We need to calculate the magnetic induction at the point O
Using formula for magnetic induction
Put the value into formula
Hence, The magnetic induction at the point O is
(a) is correct option.