Question 31: Magnetism and Matter

Question

A particle of charge $q$, mass $m$ and kinetic energy $E$ enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of $r$ with $E$ ?

Accepted Answer

$$\begin{aligned}
& \frac{\mathrm{mv}^2}{\mathrm{r}}=\mathrm{qvB} \
& \mathrm{mv}=\mathrm{qBr} \
& \mathrm{E}=\frac{1}{2} \mathrm{mv}^2 \
& \mathrm{E}=\frac{1}{2} \mathrm{~m}\left(\frac{\mathrm{q}^2 \mathrm{~B}^2 \mathrm{r}^2}{\mathrm{~m}^2}ight)=\frac{\mathrm{q}^2 \mathrm{~B}^2 \mathrm{r}^2}{2 \mathrm{~m}} \
& \mathrm{E}=\left(\frac{\mathrm{q}^2 \mathrm{~B}^2}{2 \mathrm{~m}}ight) \mathrm{r}^2 \
& \mathrm{r}^2 \propto \mathrm{E}
\end{aligned}$$

Answer

Answer

Answer

Answer

Magnetism and Matter

A particle of charge q, mass m and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius (r). Which of the following curves represents the variation of r with E ?

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