A proton (mass m and charge +e) and an alpha- | vedclass

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(C) The radius $r$ of a charged particle moving in a uniform magnetic field $B$ with kinetic energy $K$ is given by the formula $r = \frac{\sqrt{2mK}}

Vedclass · Accepted Answer

The $\alpha$-particle and the proton will be bent in a circular path with the same radius.

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(C) The radius $r$ of a charged particle moving in a uniform magnetic field $B$ with kinetic energy $K$ is given by the formula $r = \frac{\sqrt{2mK}}{qB}$.Since $K$ and $B$ are the same for both particles,we have $r \propto \frac{\sqrt{m}}{q}$.For the proton: $m_p = m$ and $q_p = e$. Thus,$r_p \propto \frac{\sqrt{m}}{e}$.For the $\alpha$-particle: $m_{\alpha} = 4m$ and $q_{\alpha} = 2e$. Thus,$r_{\alpha} \propto \frac{\sqrt{4m}}{2e} = \frac{2\sqrt{m}}{2e} = \frac{\sqrt{m}}{e}$.Comparing the two,we find that $r_p = r_{\alpha}$.Therefore,both particles will move in a circular path with the same radius.

$A$ proton (mass $m$ and charge $+e$) and an $\alpha$-particle (mass $4m$ and charge $+2e$) are projected with the same kinetic energy at right angles to a uniform magnetic field. Which one of the following statements will be true?

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