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  4. A current-carrying wire of certain length is bent to form an arc that subtends an angle θ at the centre. Let B be the magnetic field at the centre due to this wire. The correct graph between B and θ is

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Q. A current-carrying wire of certain length is bent to form an arc that subtends an angle $\theta $ at the centre. Let $B$ be the magnetic field at the centre due to this wire. The correct graph between $B$ and $\theta $ is

NTA AbhyasNTA Abhyas 2020Moving Charges and Magnetism

Solution:

$\frac{l}{R}=\theta $
$B=\frac{\mu_0 i \theta}{2 \pi(2 R)}$
$B=\frac{\mu _{0} i l \theta ^{2}}{4 \pi l^{2}}$
$B \propto \theta ^{2}$