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Question Number 38376 by ajfour last updated on 24/Jun/18

Commented by MrW3 last updated on 25/Jun/18

$${what}^{\prime }sthequestion?$$

Commented by ajfour last updated on 25/Jun/18

$$positionvectoroftheparticle$$$$asafunctionoftime,\overline{r}\left(t\right)=?$$$$Considerthecurrentcarrying$$$$wiretobeverylongandgravity$$$$present.$$

Answered by ajfour last updated on 25/Jun/18

$$Magneticfieldat(x,y)is$$$$B=-\frac{{\mu }_{0}I}{2\pi x}\hat{k}$$$$letvelocityatP(x,y)be$$$$\overline{v}=v_x\hat{i}+v_y\hat{j}$$$$\overline{F}=-mg\hat{j}+\frac{{\mu }_{0}Iq}{2\pi x}(-v_y\hat{i}+v_x\hat{j})$$$$m(\frac{{dv}_x}{dt}\hat{i}+\frac{{dv}_y}{dt}\hat{j})=-mg\hat{j}+\frac{{\mu }_{0}Iq}{2\pi x}(-v_y\hat{i}+v_x\hat{j})$$$$\frac{{dv}_x}{dt}=-\frac{{\mu }_0{Iqv}_y}{2\pi x}$$$$\frac{{dv}_y}{dt}=-mg+\frac{{\mu }_0{Iqv}_x}{2\pi x}$$$$....?$$

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