Question

Derive an expression for the magnetic field B, due to a circular coil of N turns, each of radius r carrying current I, at a distance ' x ' from the…

Accepted Answer

The magnitude of the magnetic field d B due to the current element I d l is d B =(μ 0)/(4 π) (I d l × a )/(a^3) d B =(μ 0)/(4 π) (I d l)/(( r^2+ x^2)) The components of the magnetic field perpendicular to the x-axis (d B ⊥) are summed over and get cancelled. The components of the magnetic field along the x-axis contribute towards the net magnetic field: B x =∫ d B cos θ=∫ (μ 0)/(4 π) (I d l)/(( x^2+ r^2)) · r √ x^2+ r^2 B = B x =(μ 0 I r^2)/(2( x^2+ r^2)^3 / 2)( ) For N number of turns, net magnetic field B net =(μ 0 NIr^2)/(2( x^2+ r^2)^3 / 2)( i )

Derive an expression for the magnetic field $\displaystyle \overrightarrow{\mathrm{B}}$, due to a circular coil of N turns, each of radius r carrying current I, at a distance ' $\displaystyle \mathrm{x}$ ' from the centre along its axis.

Marking-scheme solution

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