    Question

# 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

A
5
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B
10
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C
20
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D
25
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Solution

## The correct option is C 20The magnetic field at the center of a current carrying circular loop of radius R is: Bcenter=μ0i2RThe magnetic field on the axis at a distance x from the center of a current carrying circular loop of radius R is: Baxis=μ0iR22(R2+x2)3/2Given Bcenter=5√5Baxis∴μ0i2R=5√5μ0iR22(R2+x2)3/2⇒(R2+x2)3R6=(5√5)2=125⇒(R2+x2R2)3=125⇒R2+x2R2=5⇒1+x2R2=5x2R2=4 x=2R=2×10=20cm since given R=10cm  Suggest Corrections  0      Similar questions  Related Videos   Magnetic Field Due to a Current Carrying Wire
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