KCET · Physics · Magnetic Effects of Current
An \(\alpha\)-particle and a proton moving with the same kinetic energy enter a region of uniform magnetic field at right angles to the field. The ratio of the radii of the paths of \(\alpha\)-particle to that of the proton is
- A \(1: 8\)
- B \(1: 1\)
- C \(1: 2\)
- D \(1: 4\)
Answer & Solution
Correct Answer
(B) \(1: 1\)
Step-by-step Solution
Detailed explanation
Radius of circular path of charged particle in uniform magnetic field
\(\mathrm{r} =\frac{\mathrm{P}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{mK}}}{\mathrm{qB}} \)
\(\therefore \mathrm{r}: \mathrm{r}_{2} =\frac{\sqrt{\mathrm{m}_{1}}}{\mathrm{q}_{1}}: \frac{\sqrt{\mathrm{m}_{2}}}{\mathrm{q}_{2}} \)
\(=\frac{\sqrt{4}}{2}: \frac{\sqrt{1}}{1}=1: 1\)
\(\mathrm{r} =\frac{\mathrm{P}}{\mathrm{qB}}=\frac{\sqrt{2 \mathrm{mK}}}{\mathrm{qB}} \)
\(\therefore \mathrm{r}: \mathrm{r}_{2} =\frac{\sqrt{\mathrm{m}_{1}}}{\mathrm{q}_{1}}: \frac{\sqrt{\mathrm{m}_{2}}}{\mathrm{q}_{2}} \)
\(=\frac{\sqrt{4}}{2}: \frac{\sqrt{1}}{1}=1: 1\)
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