Find the magnetic field due to a semi-infinit | vedclass

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Question

(A) The magnetic field $B$ at a distance $d$ from a finite wire carrying current $I$ subtending angles $	heta_1$ and $	heta_2$ at point $P$ is given

Vedclass · Accepted Answer

$B_p = \frac{{\mu _0}I}{{4\pi d}}[\sin 	heta + 1]$

Vedclass · Answer

(A) The magnetic field $B$ at a distance $d$ from a finite wire carrying current $I$ subtending angles $	heta_1$ and $	heta_2$ at point $P$ is given by $B = \frac{{\mu _0}I}{{4\pi d}}(\sin 	heta_1 + \sin 	heta_2)$.In the given figure,the wire is semi-infinite,meaning one end is at the perpendicular projection of $P$ on the wire (angle $	heta_1 = 0^\circ$) and the other end extends to infinity (angle $	heta_2 = 90^\circ$).However,based on the geometry provided in the diagram,the angle $	heta$ is defined between the perpendicular and the line connecting $P$ to the finite end of the wire.Thus,the angles are $	heta_1 = 	heta$ and $	heta_2 = 90^\circ$.Substituting these into the formula,we get $B_p = \frac{{\mu _0}I}{{4\pi d}}(\sin 	heta + \sin 90^\circ)$.Since $\sin 90^\circ = 1$,the expression becomes $B_p = \frac{{\mu _0}I}{{4\pi d}}(\sin 	heta + 1)$.

Find the magnetic field due to a semi-infinite length wire at point $P$ as shown in the figure.

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