A long straight wire in the horizontal plane | vedclass

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Question

(A) The magnetic field $B$ produced by a long straight current-carrying wire at a distance $r$ is given by the formula:$B = \frac{\mu_0 I}{2 \pi r}$Gi

Vedclass · Accepted Answer

$4 	imes 10^{-6} \, T$ upwards

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(A) The magnetic field $B$ produced by a long straight current-carrying wire at a distance $r$ is given by the formula:$B = \frac{\mu_0 I}{2 \pi r}$Given:$I = 50 \, A$$r = 2.5 \, m$$\mu_0 = 4 \pi 	imes 10^{-7} \, T \cdot m/A$Substituting the values:$B = \frac{(4 \pi 	imes 10^{-7}) 	imes 50}{2 \pi 	imes 2.5}$$B = \frac{2 	imes 10^{-7} 	imes 50}{2.5}$$B = \frac{100 	imes 10^{-7}}{2.5} = 40 	imes 10^{-7} = 4 	imes 10^{-6} \, T$According to the Right-Hand Thumb Rule, if the current flows from North to South, and the point is to the East of the wire, the magnetic field lines curl around the wire. At a point to the East of the wire, the direction of the magnetic field is vertically upwards (out of the horizontal plane).

$A$ long straight wire in the horizontal plane carries a current of $50\, A$ in the north to south direction. Find the magnitude and direction of the magnetic field $B$ at a point $2.5\, m$ east of the wire.

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