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\mathbf{F}_m = q_0\left(\mathbf{v}_0 \times \mathbf{B} \right)

\mathbf{B}  = \mu_0\  \int \frac{I\mathrm{d}q\mathbf{\ellv} \times \hat{\mathbf{r}}}{\sigma r^2}  = \mu_0 \frac{q\mathbf{v} \times }

where:

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  body \mathbf{F}_m

  is the force induced by magnetic field

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  body \mathbf{B}

  on test charge

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  body \displaystyle q_0

  that is moving with velocity

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  body \displaystyle \mathbf{v}_0

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  body \mathbf{B}

  is the magnetic field generated by charge

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  body \displaystyle q

  moving with velocity

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  body \displaystyle \mathbf{v}

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  body \displaystyle \mathbf{r}

  is the displacement vector to moving charge

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  body \displaystyle q

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    body \displaystyle \hat{ \mathbf{r}}

    is the unit vector in the direction of

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    body \displaystyle \mathbf{r}

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    body r = \left| \mathbf{r}\right|

    is the length of

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    body \displaystyle \mathbf{

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• • r}

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  body \sigma = 2\tau = 4\pi

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  body \mu_0

  is the “vacuum inductivity” (vacuum permeability)

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