Find the magnetic field at point P in the giv | vedclass

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Question

(A) The magnetic field due to a finite wire at a perpendicular distance $r$ is given by $B = \frac{\mu_0 i}{4\pi r}(\sin 	heta_1 + \sin 	heta_2)$.Al

Vedclass · Accepted Answer

$\frac{\mu_0 i}{4\pi a}(\sqrt{3} - 1) \odot $

Vedclass · Answer

(A) The magnetic field due to a finite wire at a perpendicular distance $r$ is given by $B = \frac{\mu_0 i}{4\pi r}(\sin 	heta_1 + \sin 	heta_2)$.Alternatively,using the angles $\alpha_1$ and $\alpha_2$ with the wire,the formula is $B = \frac{\mu_0 i}{4\pi r}(\cos \alpha_1 - \cos \alpha_2)$.From the diagram,the perpendicular distance from $P$ to the wire is $r = a \sin 30^{\circ} = a/2$.The angles are $\alpha_1 = 30^{\circ}$ and $\alpha_2 = 60^{\circ}$.Substituting these values: $B = \frac{\mu_0 i}{4\pi (a/2)}(\cos 30^{\circ} - \cos 60^{\circ})$.$B = \frac{\mu_0 i}{2\pi a}(\frac{\sqrt{3}}{2} - \frac{1}{2}) = \frac{\mu_0 i}{4\pi a}(\sqrt{3} - 1) \odot $.

Find the magnetic field at point $P$ in the given diagram.

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