Assertion : A proton and an alpha particle having same kinetic energy are moving in circular paths i

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4.Moving Charges and Magnetism

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Assertion : A proton and an alpha particle having the same kinetic energy are moving in circular paths in a uniform magnetic field. The radii of their circular paths will be equal.

Reason : Any two charged particles having equal kinetic energies and entering a region of uniform magnetic field $\overrightarrow B $ in a direction perpendicular to $\overrightarrow B $, will describe circular trajectories of equal radii.

If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

If Assertion is correct but Reason is incorrect.

If both the Assertion and Reason are incorrect.

(AIIMS-2009)

Solution

The radius of the circular path is given by

$r=\frac{m v}{q B}=\frac{\sqrt{2 m K}}{q B} ;$ where $K=\frac{1}{2} m v^{2}$

since $K$ and $B$ are the same for the two particles, $r \propto \frac{\sqrt{m}}{q} .$ Now, the charge of an alpha particle is twice that of a proton and its mass is four times the mass of a proton, $\sqrt{m} / q$ will be the same for both particles. Hence, $r$ will be the same for both particles.

Standard 12

Physics

An electron and a positron are released from $(0, 0, 0)$ and $(0, 0, 1.5\, R)$ respectively, in a uniform magnetic field ${\rm{\vec B = }}{{\rm{B}}_0}{\rm{\hat i}}$ , each with an equal momentum of magnitude $P = eBR$. Under what conditions on the direction of momentum will the orbits be non-intersecting circles ?

hard

Consider the following statements regarding a charged particle in a magnetic field . Which of the statements are true :

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A beam of well collimated cathode rays travelling with a speed of $5 \times {10^6}\,m{s^{ – 1}}$ enter a region of mutually perpendicular electric and magnetic fields and emerge undeviated from this region. If $| B |=0.02\; T$, the magnitude of the electric field is

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If a charged particle goes unaccelerated in a region containing electric and magnetic fields

easy

Ionized hydrogen atoms and $\alpha$ -particles with same momenta enters perpendicular to a constant magnetic field $B$. The ratio of their radii of their paths $\mathrm{r}_{\mathrm{H}}: \mathrm{r}_{\alpha}$ will be

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(NEET-2019)

Solution

Similar Questions

Consider the following statements regarding a charged particle in a magnetic field . Which of the statements are true :

A beam of well collimated cathode rays travelling with a speed of $5 \times {10^6}\,m{s^{ – 1}}$ enter a region of mutually perpendicular electric and magnetic fields and emerge undeviated from this region. If $| B |=0.02\; T$, the magnitude of the electric field is

If a charged particle goes unaccelerated in a region containing electric and magnetic fields

Ionized hydrogen atoms and $\alpha$ -particles with same momenta enters perpendicular to a constant magnetic field $B$. The ratio of their radii of their paths $\mathrm{r}_{\mathrm{H}}: \mathrm{r}_{\alpha}$ will be

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