Question

The magnetic field B due to a current carrying circular loop of radius 12cm at its centre is 0.5xx10^-4T. Find the magnetic field due to this loop at a point on the axis at a distance of 5.0cm from the centre.

Answer 1

Given :

Magnetic field at centre of circular loop is 0.5×10^-4 T

Radius of circular loop is 12 cm i.e. 0.12 m

To Find :

Magnetic field due to circular loop at distance 5 cm from centre

Solution :

•Magnetic field due to current carrying circular loop on its axis is

B = (μ•IR²)/2(R²+x²)^³/²

•Where , B is magnetic field b

I is current through the loop

R is radius of the circular loop

& x is distance of point on axis of circular loop

•Now at the centre of circular loop i.e. for x = 0

•B(centre) = (μ•I)/2R

so, 0.5×10^-4 = (μ•I)/2R

=> (μ•I)/2 = 0.5 × 0.12 × 10^-⁴

______________(1)

•Now , at distance of 5 cm i.e. 0.05m from centre on the axis of circular loop

B = (μ•IR²)/2(R²+x²)^³/²

B = 0.5×0.12×10^-⁴ (0.12)²/

[(0.12)²+(0.05)²]^³/²

B = (8640×10^-¹¹)/(0.13)³

B = (8640×10^-¹¹)/(2197×10^-6)

B = 0.3932 × 10^-⁴ T

•Magnetic field at distance of 5 cm i.e. 0.05m from centre on the axis of circular loop is 0.3932 × 10^-⁴ T