The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5√5 times the magnetic field at a point on its axis. The distance of the point from the centre of the coil (in cm) is
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Answer:
Moving Charges and Magnetism
Magnetic Field on the Axis of a Circular Current Loop
The magnetic induction at t...
PHYSICS
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Asked on December 30, 2019 by
Sparsh Morye
The magnetic induction at the centre of a current carrying circular coil of radius 10cm is 5
5
times the magnetic induction at a point on its axis. The distance of the point from the centre of the coil in cm is
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VIDEO EXPLANATION
ANSWER
The magnetic field at the center of a current carrying circular loop of radius R is: B
center
=
2R
μ
0
i
The magnetic field on the axis at a distance x from the center of a current carrying circular loop of radius R is: B
axis
=
2(R
2
+x
2
)
3/2
μ
0
iR
2
Given B
center
=5
5
B
axis
∴
2R
μ
0
i
=5
5
2(R
2
+x
2
)
3/2
μ
0
iR
2
⇒
R
6
(R
2
+x
2
)
3
=(5
5
)
2
=125
⇒(
R
2
R
2
+x
2
)
3
=125
⇒
R
2
R
2
+x
2
=5
⇒1+
R
2
x
2
=5
R
2
x
2
=4
x=2R=2×10=20cm since given R=10cm