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tiagobt

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**Niels Bohr atom and magnetic fields**

Could anyone help me solve the following problem?

I am supposed to use Biot-Savart Law. What I tried was:According to 1913 Niels Bohr hydrogen atom model, an electron orbits a proton from a distance of [itex]5.29 \times 10^{-11} m[/itex] with a velocity of [itex]2.19 \times 10^6 m/s[/itex]. Find the intensity of the magnetic field produced by this movement in the position of the proton.

The orbit of the electron can be interpreted as a current flowing in a circular spire (on the opposite direction of the electron's velocity). If an element [itex]d \vec{s}[/itex] of the spire produces a field [itex]d \vec{B}[/itex] in the position of the proton, the intensity of [itex] d \vec{B}[/itex] can be written as the following:

[itex]dB = \frac{\mu_0ids}{4 \pi R^2}[/itex]

[itex]B = \frac{\mu_0i}{4 \pi R^2} \oint ds[/itex]

Calculating the integral for the entire circle:

[itex]B = \frac{\mu_0i2 \pi R}{4 \pi R^2} = \frac{\mu_0i}{2R}[/itex]

And then I tried to calculate the electical current as a function of the electron's velocity of displacement:

[itex]i = nq_{e}v_{d}A[/itex]

Where [itex]n[/itex] is the number of free charged particles, [itex]q_e[/itex] is the charge of an electron, [itex]v_d[/itex] is the velocity of displacement of the charge and [itex]A[/itex] is the area of section of the current conductor. I am not sure what [itex]A[/itex] could be in the original problem. Am I making any sense?

Thanks,

Tiago

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