An electron of mass m and charge q is travelling with a speed v along a circular path of radius r at right angles to a uniform of magnetic field B. If speed of the electron is doubled and the magnetic field is halved, then resulting path would have a radius of

(a) $\frac{r}{4}$                           (b) $\frac{r}{2}$

(c) $2r$                            (d) $4r$

(d)   $r=\frac{mv}{qB}⇒\frac{{r}_{1}}{{r}_{2}}=\frac{{v}_{1}}{{v}_{2}}×\frac{{B}_{2}}{{B}_{1}}⇒\frac{{r}_{1}}{{r}_{2}}=\frac{1}{2}×\frac{1}{2}=\frac{1}{4}\phantom{\rule{0ex}{0ex}}{r}_{2}=4{r}_{1}$

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