IV. (a) Using Biot-savart's law, find the magnetic field (intensity) due
to a carrent carrying loop at a point on the axis passes through the
centre and perpendicular to the plane of the loop.
Answers
Answer:
According to Biot-Savart Law, magnetic field due to a current carrying element dl is:
dB
=
4πr
3
μ
o
I
(
dl
×
r
)
The magnetic field due to a current carrying circular loop is shown in the figure. Vertical components of the magnetic field cancel out by the diametrically opposite end on the wire.
Horizontal component due to an element dl is given by:
dB=
4πr
2
μ
o
I
sinθdl
dB=
4πr
3
μ
o
IR
dl
∫dB=
4πr
3
μ
o
IR
∫dl
B=
4π(R
2
+x
2
)
3/2
μ
o
IR
2πR
B=
2(R
2
+x
2
)
3/2
μ
o
IR
2
(b)
From Biot-Savart Law, it can be concluded that the magnetic field around an infinitely long current carrying conductor is
B=
2πr
μ
o
I
or B×2πr=μ
o
I
∫B.dl=μ
o
I