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KCET2017PhysicsCapacitance

The magnetic field at the center of a current carrying loop of radius ( 0.1 ~m ) is ( 5 5 ) times that at a point along its axis. The distance of this point from the centre of the loop is

Options

  1. A( 0.2 ~m )
  2. B( 0.1 ~m )
  3. C( 0.05 ~m )
  4. D( 0.25 ~m )

Correct answer

A. ( 0.2 ~m )

Step-by-step solution

Magnetic field at the centre of current carrying loop is given as B_ C = ₀ 2 I r Magnetic field at the axis is given as B_ A = ₀ 2 I r² ( ²+r² )^ 3 / 2 Given, B_ C =5 5 B_ A ₀ 2 I r =5 5 ₀ 2 I r² ( ²+r² )^ 3 / 2 (x²+r² )^ 3 / 2 =r³ 5 5 (x²+r² )^ 3 / 2 =r³ 5^ 3 / 2 ²+r²=r² 5 ²=5 r²-r² ²=4 r² or x=2 r Given, r=0.1 ~m =0.2 m

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