Using the formula from , find the distribution of magnetic field induction around an infinite charged thread with a linear charge density \rho if the thread moves in the longitudinal direction with a velocity v.

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    <h3 id="back-link"><a href="/#9.2">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $9.2.2.$ Using the formula from <a href="/9.2.1" target = "_blank">the previous problem</a>, find the distribution of magnetic field induction around an infinite charged thread with a linear charge density $\rho$ if the thread moves in the longitudinal direction with a velocity $v$.
    </p>

    <h3>Solution</h3>
    <p>
        Field $E$ of an infinite charged thread

$$E = \frac{1}{2\pi\varepsilon_0 }\cdot \frac{\rho}{r}$$
then we find the induction distribution of the magnetic field induction around an infinite charged thread
$$|\vec{B}| = \varepsilon_0 \mu_0|\vec{v}\times \vec{E}| = \varepsilon_0 \mu_0 vE$$
Substituting the expression for $E$ and after transformations, we obtain the final formula for the magnetic field modulus:
$$\boxed{|\vec{B}| = \frac{\mu_0}{2\pi} \cdot \frac{\rho v}{r}}$$

    </p>

    <h4>Answer</h4>
    <p>
        $$B = \frac{\mu_0}{2\pi} \cdot \frac{\rho v}{r}$$
    </p>
	<p style="text-align: right; font-style: italic; font-size: 14;">
      Andrei Yersh<br>
    </p>


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