Question

The magnetic field at the center of a current carrying loop of radius 0.1 m is 55 times that at a point along its axis. The distance of this point from the centre of the loop is (A) 0.1 m (B) 0.2 m (C) 0.05 m (D) 0.25 m

Answer 1

Answer:

0.2 m

Explanation:

Given 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

We know that magnetic field  µo i / 2 r = µo I r^2 / 2(x^2 + r^2)^3/2

Now according to question, we have µo i / 2 r = 5√5 µo I r^2 / 2(x^2 + r^2)^3/2

 So 1/r^3 = 5√5 / (x^2 + r^2)^3/2

We can write as  

 5√5 r^3 = (x^2 + r^2)^3/2

Squaring both sides we get

  125 r^6 = (x^2 + r^2)^3

  (5 r^2)^3 = (x^2 + r^2)^3

 X^2 + r^2 = 5 r^2

  X^2 = 4 r^2

 X = + 2 r

 Given radius = 10 cm

 So x = 2 x 0.1 = 0.2 m

The distance of this point from the centre of the loop is 0.2 m