A proton, a deuteron, and an alpha-particle a | vedclass

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(B) The magnetic force on a charged particle is given by $F = qvB \sin 	heta$. Since the momentum $P = mv$ is constant, we can write $v = P/m$. Subst

Vedclass · Accepted Answer

$2: 1: 1$ and $4: 2: 1$

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(B) The magnetic force on a charged particle is given by $F = qvB \sin 	heta$. Since the momentum $P = mv$ is constant, we can write $v = P/m$. Substituting this, $F = q(P/m)B = (P B) \cdot (q/m)$.Since $P$ and $B$ are constant, $F \propto q/m$.For a proton $(p)$, deuteron $(d)$, and $\alpha$-particle $(\alpha)$:$q_p = e, m_p = m$$q_d = e, m_d = 2m$$q_{\alpha} = 2e, m_{\alpha} = 4m$Ratio of forces $F_p : F_d : F_{\alpha} = \frac{e}{m} : \frac{e}{2m} : \frac{2e}{4m} = 1 : \frac{1}{2} : \frac{1}{2} = 2 : 1 : 1$.For speed, $P = mv \Rightarrow v = P/m$. Since $P$ is constant, $v \propto 1/m$.Ratio of speeds $v_p : v_d : v_{\alpha} = \frac{1}{m} : \frac{1}{2m} : \frac{1}{4m} = 1 : \frac{1}{2} : \frac{1}{4} = 4 : 2 : 1$.

$A$ proton, a deuteron, and an $\alpha$-particle are moving with the same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is.......... and their speeds are in the ratio of..........

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