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A long straight copper wire carries current in an upward direction. If a charge of 25 kC passes at a point within 0.5 s, determine the magnitude of the current induced at the point and the magnitude and direction of the magnetic field produced at point P where point P is 275 cm to the right of the wire.

Respuesta :

The current induce at the point can be given as,

[tex]I=\frac{q}{t}[/tex]

Plug in the known values,

[tex]\begin{gathered} I=\frac{(25\text{ kC)(}\frac{1000\text{ C}}{1\text{ kC}})}{0.5\text{ s}}(\frac{1\text{ A}}{1\text{ C/s}}) \\ =50000\text{ A} \end{gathered}[/tex]

The magnetic field produced at the point P is given as,

[tex]B=\frac{\mu_0I}{2\pi r}[/tex]

Substituting values,

[tex]\begin{gathered} B=\frac{(4\pi\times10^{-7}\text{ Tm/A)(50000 A)}}{2\pi(275\text{ cm)(}\frac{1\text{ m}}{100\text{ cm}})} \\ \approx3.63\times10^{-3}\text{ T} \end{gathered}[/tex]

Therefore, the current induced in the wire is 50000 A, the magnetic field acting on the point is

[tex]3.63\times10^{-3}\text{ T}[/tex]

which acts in the anticlockwise direction as the current moves in the upward direction.