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The magnetic field at the centre of a current carrying circular coil of radius 10 cm is 5 root 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? 1. 5 2.10 3.20 4.25?
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The magnetic field at the centre of a current carrying circular coil o...
Solution:

Given:

Radius of circular coil, r = 10 cm

Magnetic field at the centre of the coil, Bc = 5√5 Bx

We need to find the distance of the point from the centre of the coil, where the magnetic field is Bx.

Let us assume that the point is at a distance of x cm from the centre of the coil.

Magnetic field at the centre of the coil:

The magnetic field at the centre of a current carrying circular loop of radius r is given by:

Bc = µ0 I / (2r)

Where,

µ0 is the permeability of free space

I is the current flowing in the loop

r is the radius of the loop

Substituting the given values, we get:

5√5 Bx = µ0 I / (2r)

∴ Bx = (µ0 I) / (10√5)

Magnetic field on the axis of the coil:

The magnetic field on the axis of a current carrying circular loop at a distance x from the centre of the loop is given by:

Bx = (µ0 I / 2) * (R2 / (R2 + x2)3/2)

Where,

R is the radius of the loop

Substituting the given values, we get:

5√5 Bx = (µ0 I / 2) * (100 / (100 + x2)3/2)

∴ Bx = (µ0 I) / (10√5 * (100 + x2)3/2)

Equating Bx from both the equations:

(µ0 I) / (10√5) = (µ0 I) / (10√5 * (100 + x2)3/2)

∴ (100 + x2)3/2 = 1

∴ 100 + x2 = 1

∴ x = √99 = 3√11 cm

Therefore, the distance of the point from the centre of the coil is 3√11 cm, which is approximately equal to 5.3 cm.

Hence, the correct option is 4. 25.
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The magnetic field at the centre of a current carrying circular coil o...
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